PK_Mqtddpygam/__init__.py""" GAM toolkit """ from __future__ import absolute_import from pygam.pygam import GAM from pygam.pygam import LinearGAM from pygam.pygam import LogisticGAM from pygam.pygam import GammaGAM from pygam.pygam import PoissonGAM from pygam.pygam import InvGaussGAM from pygam.pygam import ExpectileGAM from pygam.terms import l from pygam.terms import s from pygam.terms import f from pygam.terms import te from pygam.terms import intercept __all__ = ['GAM', 'LinearGAM', 'LogisticGAM', 'GammaGAM', 'PoissonGAM', 'InvGaussGAM', 'ExpectileGAM', 'l', 's', 'f', 'te', 'intercept'] __version__ = '0.8.0' PKTSM%  pygam/callbacks.py""" CallBacks """ from __future__ import absolute_import from functools import wraps import numpy as np from pygam.core import Core def validate_callback_data(method): """ wraps a callback's method to pull the desired arguments from the vars dict also checks to ensure the method's arguments are in the vars dict Parameters ---------- method : callable Returns ------- validated callable """ @wraps(method) def method_wrapper(*args, **kwargs): """ Parameters ---------- *args **kwargs Returns ------- method's output """ expected = method.__code__.co_varnames # rename curret gam object if 'self' in kwargs: gam = kwargs['self'] del(kwargs['self']) kwargs['gam'] = gam # loop once to check any missing missing = [] for e in expected: if e == 'self': continue if e not in kwargs: missing.append(e) assert len(missing) == 0, 'CallBack cannot reference: {}'.\ format(', '.join(missing)) # loop again to extract desired kwargs_subset = {} for e in expected: if e == 'self': continue kwargs_subset[e] = kwargs[e] return method(*args, **kwargs_subset) return method_wrapper def validate_callback(callback): """ validates a callback's on_loop_start and on_loop_end methods Parameters ---------- callback : Callback object Returns ------- validated callback """ if not(hasattr(callback, '_validated')) or callback._validated == False: assert hasattr(callback, 'on_loop_start') \ or hasattr(callback, 'on_loop_end'), \ 'callback must have `on_loop_start` or `on_loop_end` method' if hasattr(callback, 'on_loop_start'): setattr(callback, 'on_loop_start', validate_callback_data(callback.on_loop_start)) if hasattr(callback, 'on_loop_end'): setattr(callback, 'on_loop_end', validate_callback_data(callback.on_loop_end)) setattr(callback, '_validated', True) return callback class CallBack(Core): """CallBack class""" def __init__(self, name=None): """ creates a CallBack instance Parameters ---------- None Returns ------- None """ super(CallBack, self).__init__(name=name) @validate_callback class Deviance(CallBack): """Deviance CallBack class""" def __init__(self): """ creates a Deviance CallBack instance useful for capturing the Deviance of a model on training data at each iteration Parameters ---------- None Returns ------- None """ super(Deviance, self).__init__(name='deviance') def on_loop_start(self, gam, y, mu): """ runs the method at loop start Parameters ---------- gam : GAM instance y : array-like of length n target data mu : array-like of length n expected value data Returns ------- deviance : np.array of length n """ return gam.distribution.deviance(y=y, mu=mu, scaled=False).sum() @validate_callback class Accuracy(CallBack): def __init__(self): """ creates an Accuracy CallBack instance useful for capturing the accuracy of a model on training data at each iteration Parameters ---------- None Returns ------- None """ super(Accuracy, self).__init__(name='accuracy') def on_loop_start(self, y, mu): """ runs the method at start of each optimization loop Parameters ---------- y : array-like of length n target data mu : array-like of length n expected value data Returns ------- accuracy : np.array of length n """ return np.mean(y == (mu>0.5)) @validate_callback class Diffs(CallBack): def __init__(self): """ creates a Diffs CallBack instance useful for capturing the differences in model coefficient norms between iterations Parameters ---------- None Returns ------- None """ super(Diffs, self).__init__(name='diffs') def on_loop_end(self, diff): """ runs the method at end of each optimization loop Parameters ---------- diff : float Returns ------- diff : float """ return diff @validate_callback class Coef(CallBack): def __init__(self): """ creates a Coef CallBack instance useful for capturing the models coefficients at each iteration Parameters ---------- None Returns ------- None """ super(Coef, self).__init__(name='coef') def on_loop_start(self, gam): """ runs the method at start of each optimization loop Parameters ---------- gam : float Returns ------- coef_ : list of floats """ return gam.coef_ CALLBACKS = {'deviance': Deviance, 'diffs': Diffs, 'accuracy': Accuracy, 'coef': Coef } PKTSMBm%% pygam/core.py""" Core classes """ from __future__ import absolute_import import numpy as np from pygam.utils import round_to_n_decimal_places, flatten def nice_repr(name, param_kvs, line_width=30, line_offset=5, decimals=3, args=None, flatten_attrs=True): """ tool to do a nice repr of a class. Parameters ---------- name : str class name param_kvs : dict dict containing class parameters names as keys, and the corresponding values as values line_width : int desired maximum line width. default: 30 line_offset : int desired offset for new lines default: 5 decimals : int number of decimal places to keep for float values default: 3 Returns ------- out : str nicely formatted repr of class instance """ if not param_kvs and not args : # if the object has no params it's easy return '{}()'.format(name) # sort keys and values ks = list(param_kvs.keys()) vs = list(param_kvs.values()) idxs = np.argsort(ks) param_kvs = [(ks[i],vs[i]) for i in idxs] if args is not None: param_kvs = [(None, arg) for arg in args] + param_kvs param_kvs = param_kvs[::-1] out = '' current_line = name + '(' while len(param_kvs) > 0: # flatten sub-term properties, but not `terms` k, v = param_kvs.pop() if flatten_attrs and k is not 'terms': v = flatten(v) # round the floats first if issubclass(v.__class__, (float, np.ndarray)): v = round_to_n_decimal_places(v, n=decimals) v = str(v) else: v = repr(v) # handle args if k is None: param = '{},'.format(v) else: param = '{}={},'.format(k, v) # print if len(current_line + param) <= line_width: current_line += param else: out += current_line + '\n' current_line = ' '*line_offset + param if len(current_line) < line_width and len(param_kvs) > 0: current_line += ' ' out += current_line[:-1] # remove trailing comma out += ')' return out class Core(object): def __init__(self, name=None, line_width=70, line_offset=3): """ creates an instance of the Core class comes loaded with useful methods Parameters ---------- name : str, default: None line_width : int, default: 70 number of characters to print on a line line_offset : int, default: 3 number of characters to indent after the first line Returns ------- self """ self._name = name self._line_width = line_width self._line_offset = line_offset if not hasattr(self, '_exclude'): self._exclude = [] if not hasattr(self, '_include'): self._include = [] def __str__(self): """__str__ method""" if self._name is None: return self.__repr__() return self._name def __repr__(self): """__repr__ method""" name = self.__class__.__name__ return nice_repr(name, self.get_params(), line_width=self._line_width, line_offset=self._line_offset, decimals=4, args=None) def get_params(self, deep=False): """ returns a dict of all of the object's user-facing parameters Parameters ---------- deep : boolean, default: False when True, also gets non-user-facing paramters Returns ------- dict """ attrs = self.__dict__ for attr in self._include: attrs[attr] = getattr(self, attr) if deep is True: return attrs return dict([(k,v) for k,v in list(attrs.items()) \ if (k[0] != '_') \ and (k[-1] != '_') \ and (k not in self._exclude)]) def set_params(self, deep=False, force=False, **parameters): """ sets an object's paramters Parameters ---------- deep : boolean, default: False when True, also sets non-user-facing paramters force : boolean, default: False when True, also sets parameters that the object does not already have **parameters : paramters to set Returns ------ self """ param_names = self.get_params(deep=deep).keys() for parameter, value in parameters.items(): if (parameter in param_names or force or (hasattr(self, parameter) and parameter == parameter.strip('_'))): setattr(self, parameter, value) return self PKTSM<;CCpygam/distributions.py""" Distributions """ from __future__ import division, absolute_import from functools import wraps from abc import ABCMeta from abc import abstractmethod import scipy as sp import numpy as np from pygam.core import Core from pygam.utils import ylogydu def multiply_weights(deviance): @wraps(deviance) def multiplied(self, y, mu, weights=None, **kwargs): if weights is None: weights = np.ones_like(mu) return deviance(self, y, mu, **kwargs) * weights return multiplied def divide_weights(V): @wraps(V) def divided(self, mu, weights=None, **kwargs): if weights is None: weights = np.ones_like(mu) return V(self, mu, **kwargs) / weights return divided class Distribution(Core): __metaclass__ = ABCMeta """ base distribution class """ def __init__(self, name=None, scale=None): """ creates an instance of the Distribution class Parameters ---------- name : str, default: None scale : float or None, default: None scale/standard deviation of the distribution Returns ------- self """ self.scale = scale self._known_scale = self.scale is not None super(Distribution, self).__init__(name=name) if not self._known_scale: self._exclude += ['scale'] def phi(self, y, mu, edof, weights): """ GLM scale parameter. for Binomial and Poisson families this is unity for Normal family this is variance Parameters ---------- y : array-like of length n target values mu : array-like of length n expected values edof : float estimated degrees of freedom weights : array-like shape (n,) or None, default: None sample weights if None, defaults to array of ones Returns ------- scale : estimated model scale """ if self._known_scale: return self.scale else: return (np.sum(weights * self.V(mu)**-1 * (y - mu)**2) / (len(mu) - edof)) @abstractmethod def sample(self, mu): """ Return random samples from this distribution. Parameters ---------- mu : array-like of shape n_samples or shape (n_simulations, n_samples) expected values Returns ------- random_samples : np.array of same shape as mu """ pass class NormalDist(Distribution): """ Normal Distribution """ def __init__(self, scale=None): """ creates an instance of the NormalDist class Parameters ---------- scale : float or None, default: None scale/standard deviation of the distribution Returns ------- self """ super(NormalDist, self).__init__(name='normal', scale=scale) def log_pdf(self, y, mu, weights=None): """ computes the log of the pdf or pmf of the values under the current distribution Parameters ---------- y : array-like of length n target values mu : array-like of length n expected values weights : array-like shape (n,) or None, default: None sample weights if None, defaults to array of ones Returns ------- pdf/pmf : np.array of length n """ if weights is None: weights = np.ones_like(mu) scale = self.scale / weights return sp.stats.norm.logpdf(y, loc=mu, scale=scale) @divide_weights def V(self, mu): """ glm Variance function. if Y ~ ExpFam(theta, scale=phi) such that E[Y] = mu = b'(theta) and Var[Y] = b''(theta) * phi / w then we seek V(mu) such that we can represent Var[y] as a fn of mu: Var[Y] = V(mu) * phi ie V(mu) = b''(theta) / w Parameters ---------- mu : array-like of length n expected values Returns ------- V(mu) : np.array of length n """ return np.ones_like(mu) @multiply_weights def deviance(self, y, mu, scaled=True): """ model deviance for a gaussian linear model, this is equal to the SSE Parameters ---------- y : array-like of length n target values mu : array-like of length n expected values scaled : boolean, default: True whether to divide the deviance by the distribution scaled Returns ------- deviances : np.array of length n """ dev = (y - mu)**2 if scaled: dev /= self.scale return dev def sample(self, mu): """ Return random samples from this Normal distribution. Samples are drawn independently from univariate normal distributions with means given by the values in `mu` and with standard deviations equal to the `scale` attribute if it exists otherwise 1.0. Parameters ---------- mu : array-like of shape n_samples or shape (n_simulations, n_samples) expected values Returns ------- random_samples : np.array of same shape as mu """ standard_deviation = self.scale**0.5 if self.scale else 1.0 return np.random.normal(loc=mu, scale=standard_deviation, size=None) class BinomialDist(Distribution): """ Binomial Distribution """ def __init__(self, levels=1): """ creates an instance of the Binomial class Parameters ---------- levels : int of None, default: 1 number of trials in the binomial distribution Returns ------- self """ if levels is None: levels = 1 self.levels = levels super(BinomialDist, self).__init__(name='binomial', scale=1.) self._exclude.append('scale') def log_pdf(self, y, mu, weights=None): """ computes the log of the pdf or pmf of the values under the current distribution Parameters ---------- y : array-like of length n target values mu : array-like of length n expected values weights : array-like shape (n,) or None, default: None sample weights if None, defaults to array of ones Returns ------- pdf/pmf : np.array of length n """ if weights is None: weights = np.ones_like(mu) n = self.levels p = mu / self.levels return sp.stats.binom.logpmf(y, n, p) @divide_weights def V(self, mu): """ glm Variance function computes the variance of the distribution Parameters ---------- mu : array-like of length n expected values Returns ------- variance : np.array of length n """ return mu * (1 - mu / self.levels) @multiply_weights def deviance(self, y, mu, scaled=True): """ model deviance for a bernoulli logistic model, this is equal to the twice the negative loglikelihod. Parameters ---------- y : array-like of length n target values mu : array-like of length n expected values scaled : boolean, default: True whether to divide the deviance by the distribution scaled Returns ------- deviances : np.array of length n """ dev = 2 * (ylogydu(y, mu) + ylogydu(self.levels - y, self.levels - mu)) if scaled: dev /= self.scale return dev def sample(self, mu): """ Return random samples from this Normal distribution. Parameters ---------- mu : array-like of shape n_samples or shape (n_simulations, n_samples) expected values Returns ------- random_samples : np.array of same shape as mu """ number_of_trials = self.levels success_probability = mu / number_of_trials return np.random.binomial(n=number_of_trials, p=success_probability, size=None) class PoissonDist(Distribution): """ Poisson Distribution """ def __init__(self): """ creates an instance of the PoissonDist class Parameters ---------- None Returns ------- self """ super(PoissonDist, self).__init__(name='poisson', scale=1.) self._exclude.append('scale') def log_pdf(self, y, mu, weights=None): """ computes the log of the pdf or pmf of the values under the current distribution Parameters ---------- y : array-like of length n target values mu : array-like of length n expected values weights : array-like shape (n,) or None, default: None containing sample weights if None, defaults to array of ones Returns ------- pdf/pmf : np.array of length n """ if weights is None: weights = np.ones_like(mu) # in Poisson regression weights are proportional to the exposure # so we want to pump up all our predictions # NOTE: we assume the targets are counts, not rate. # ie if observations were scaled to account for exposure, they have # been rescaled before calling this function. # since some samples have higher exposure, # they also need to have higher variance, # we do this by multiplying mu by the weight=exposure mu = mu * weights return sp.stats.poisson.logpmf(y, mu=mu) @divide_weights def V(self, mu): """ glm Variance function computes the variance of the distribution Parameters ---------- mu : array-like of length n expected values Returns ------- variance : np.array of length n """ return mu @multiply_weights def deviance(self, y, mu, scaled=True): """ model deviance for a bernoulli logistic model, this is equal to the twice the negative loglikelihod. Parameters ---------- y : array-like of length n target values mu : array-like of length n expected values scaled : boolean, default: True whether to divide the deviance by the distribution scaled Returns ------- deviances : np.array of length n """ dev = 2 * (ylogydu(y, mu) - (y - mu)) if scaled: dev /= self.scale return dev def sample(self, mu): """ Return random samples from this Poisson distribution. Parameters ---------- mu : array-like of shape n_samples or shape (n_simulations, n_samples) expected values Returns ------- random_samples : np.array of same shape as mu """ return np.random.poisson(lam=mu, size=None) class GammaDist(Distribution): """ Gamma Distribution """ def __init__(self, scale=None): """ creates an instance of the GammaDist class Parameters ---------- scale : float or None, default: None scale/standard deviation of the distribution Returns ------- self """ super(GammaDist, self).__init__(name='gamma', scale=scale) def log_pdf(self, y, mu, weights=None): """ computes the log of the pdf or pmf of the values under the current distribution Parameters ---------- y : array-like of length n target values mu : array-like of length n expected values weights : array-like shape (n,) or None, default: None containing sample weights if None, defaults to array of ones Returns ------- pdf/pmf : np.array of length n """ if weights is None: weights = np.ones_like(mu) nu = weights / self.scale return sp.stats.gamma.logpdf(x=y, a=nu, scale=mu / nu) @divide_weights def V(self, mu): """ glm Variance function computes the variance of the distribution Parameters ---------- mu : array-like of length n expected values Returns ------- variance : np.array of length n """ return mu**2 @multiply_weights def deviance(self, y, mu, scaled=True): """ model deviance for a bernoulli logistic model, this is equal to the twice the negative loglikelihod. Parameters ---------- y : array-like of length n target values mu : array-like of length n expected values scaled : boolean, default: True whether to divide the deviance by the distribution scaled Returns ------- deviances : np.array of length n """ dev = 2 * ((y - mu) / mu - np.log(y / mu)) if scaled: dev /= self.scale return dev def sample(self, mu): """ Return random samples from this Gamma distribution. Parameters ---------- mu : array-like of shape n_samples or shape (n_simulations, n_samples) expected values Returns ------- random_samples : np.array of same shape as mu """ # in numpy.random.gamma, `shape` is the parameter sometimes denoted by # `k` that corresponds to `nu` in S. Wood (2006) Table 2.1 shape = 1. / self.scale # in numpy.random.gamma, `scale` is the parameter sometimes denoted by # `theta` that corresponds to mu / nu in S. Wood (2006) Table 2.1 scale = mu / shape return np.random.gamma(shape=shape, scale=scale, size=None) class InvGaussDist(Distribution): """ Inverse Gaussian (Wald) Distribution """ def __init__(self, scale=None): """ creates an instance of the InvGaussDist class Parameters ---------- scale : float or None, default: None scale/standard deviation of the distribution Returns ------- self """ super(InvGaussDist, self).__init__(name='inv_gauss', scale=scale) def log_pdf(self, y, mu, weights=None): """ computes the log of the pdf or pmf of the values under the current distribution Parameters ---------- y : array-like of length n target values mu : array-like of length n expected values weights : array-like shape (n,) or None, default: None containing sample weights if None, defaults to array of ones Returns ------- pdf/pmf : np.array of length n """ if weights is None: weights = np.ones_like(mu) gamma = weights / self.scale return sp.stats.invgauss.logpdf(y, mu, scale=1./gamma) @divide_weights def V(self, mu): """ glm Variance function computes the variance of the distribution Parameters ---------- mu : array-like of length n expected values Returns ------- variance : np.array of length n """ return mu**3 @multiply_weights def deviance(self, y, mu, scaled=True): """ model deviance for a bernoulli logistic model, this is equal to the twice the negative loglikelihod. Parameters ---------- y : array-like of length n target values mu : array-like of length n expected values scaled : boolean, default: True whether to divide the deviance by the distribution scaled Returns ------- deviances : np.array of length n """ dev = ((y - mu)**2) / (mu**2 * y) if scaled: dev /= self.scale return dev def sample(self, mu): """ Return random samples from this Inverse Gaussian (Wald) distribution. Parameters ---------- mu : array-like of shape n_samples or shape (n_simulations, n_samples) expected values Returns ------- random_samples : np.array of same shape as mu """ return np.random.wald(mean=mu, scale=self.scale, size=None) DISTRIBUTIONS = {'normal': NormalDist, 'poisson': PoissonDist, 'binomial': BinomialDist, 'gamma': GammaDist, 'inv_gauss': InvGaussDist } PKTSMxxpygam/links.py""" Link functions """ from __future__ import division, absolute_import import numpy as np from pygam.core import Core class Link(Core): def __init__(self, name=None): """ creates an instance of a Link object Parameters ---------- name : str, default: None Returns ------- self """ super(Link, self).__init__(name=name) class IdentityLink(Link): def __init__(self): """ creates an instance of an IdentityLink object Parameters ---------- None Returns ------- self """ super(IdentityLink, self).__init__(name='identity') def link(self, mu, dist): """ glm link function this is useful for going from mu to the linear prediction Parameters ---------- mu : array-like of legth n dist : Distribution instance Returns ------- lp : np.array of length n """ return mu def mu(self, lp, dist): """ glm mean function, ie inverse of link function this is useful for going from the linear prediction to mu Parameters ---------- lp : array-like of legth n dist : Distribution instance Returns ------- mu : np.array of length n """ return lp def gradient(self, mu, dist): """ derivative of the link function wrt mu Parameters ---------- mu : array-like of legth n dist : Distribution instance Returns ------- grad : np.array of length n """ return np.ones_like(mu) class LogitLink(Link): def __init__(self): """ creates an instance of a LogitLink object Parameters ---------- None Returns ------- self """ super(LogitLink, self).__init__(name='logit') def link(self, mu, dist): """ glm link function this is useful for going from mu to the linear prediction Parameters ---------- mu : array-like of legth n dist : Distribution instance Returns ------- lp : np.array of length n """ return np.log(mu) - np.log(dist.levels - mu) def mu(self, lp, dist): """ glm mean function, ie inverse of link function this is useful for going from the linear prediction to mu Parameters ---------- lp : array-like of legth n dist : Distribution instance Returns ------- mu : np.array of length n """ elp = np.exp(lp) return dist.levels * elp / (elp + 1) def gradient(self, mu, dist): """ derivative of the link function wrt mu Parameters ---------- mu : array-like of legth n dist : Distribution instance Returns ------- grad : np.array of length n """ return dist.levels/(mu*(dist.levels - mu)) class LogLink(Link): def __init__(self): """ creates an instance of a LogitLink object Parameters ---------- None Returns ------- self """ super(LogLink, self).__init__(name='log') def link(self, mu, dist): """ glm link function this is useful for going from mu to the linear prediction Parameters ---------- mu : array-like of legth n dist : Distribution instance Returns ------- lp : np.array of length n """ return np.log(mu) def mu(self, lp, dist): """ glm mean function, ie inverse of link function this is useful for going from the linear prediction to mu Parameters ---------- lp : array-like of legth n dist : Distribution instance Returns ------- mu : np.array of length n """ return np.exp(lp) def gradient(self, mu, dist): """ derivative of the link function wrt mu Parameters ---------- mu : array-like of legth n dist : Distribution instance Returns ------- grad : np.array of length n """ return 1. / mu class InverseLink(Link): def __init__(self): """ creates an instance of a InverseLink object Parameters ---------- None Returns ------- self """ super(InverseLink, self).__init__(name='inverse') def link(self, mu, dist): """ glm link function this is useful for going from mu to the linear prediction Parameters ---------- mu : array-like of legth n dist : Distribution instance Returns ------- lp : np.array of length n """ return mu ** -1. def mu(self, lp, dist): """ glm mean function, ie inverse of link function this is useful for going from the linear prediction to mu Parameters ---------- lp : array-like of legth n dist : Distribution instance Returns ------- mu : np.array of length n """ return lp ** -1. def gradient(self, mu, dist): """ derivative of the link function wrt mu Parameters ---------- mu : array-like of legth n dist : Distribution instance Returns ------- grad : np.array of length n """ return -1 * mu**-2. class InvSquaredLink(Link): def __init__(self): """ creates an instance of an InverseLink object Parameters ---------- name : str, default: None Returns ------- self """ super(InvSquaredLink, self).__init__(name='inv_squared') def link(self, mu, dist): """ glm link function this is useful for going from mu to the linear prediction Parameters ---------- mu : array-like of legth n dist : Distribution instance Returns ------- lp : np.array of length n """ return mu ** -2. def mu(self, lp, dist): """ glm mean function, ie inverse of link function this is useful for going from the linear prediction to mu Parameters ---------- lp : array-like of legth n dist : Distribution instance Returns ------- mu : np.array of length n """ return lp ** -0.5 def gradient(self, mu, dist): """ derivative of the link function wrt mu Parameters ---------- mu : array-like of legth n dist : Distribution instance Returns ------- grad : np.array of length n """ return -2 * mu**-3. LINKS = {'identity': IdentityLink, 'log': LogLink, 'logit': LogitLink, 'inverse': InverseLink, 'inv_squared': InvSquaredLink } PKde_MՂ%%pygam/penalties.py""" Penalty matrix generators """ import scipy as sp import numpy as np def derivative(n, coef, derivative=2, periodic=False): """ Builds a penalty matrix for P-Splines with continuous features. Penalizes the squared differences between basis coefficients. Parameters ---------- n : int number of splines coef : unused for compatibility with constraints derivative: int, default: 2 which derivative do we penalize. derivative is 1, we penalize 1st order derivatives, derivative is 2, we penalize 2nd order derivatives, etc Returns ------- penalty matrix : sparse csc matrix of shape (n,n) """ if n == 1: # no derivative for constant functions return sp.sparse.csc_matrix(0.) D = sparse_diff(sp.sparse.identity(n + 2*derivative*periodic).tocsc(), n=derivative).tolil() if periodic: # wrap penalty cols = D[:, :derivative] D[:, -2 * derivative:-derivative] += cols * (-1) ** derivative # do symmetric operation on lower half of matrix n_rows = int((n + 2 * derivative)/2) D[-n_rows:] = D[:n_rows][::-1, ::-1] # keep only the center of the augmented matrix D = D[derivative:-derivative, derivative:-derivative] return D.dot(D.T).tocsc() def periodic(n, coef, derivative=2, _penalty=derivative): return _penalty(n, coef, derivative=derivative, periodic=True) def l2(n, coef): """ Builds a penalty matrix for P-Splines with categorical features. Penalizes the squared value of each basis coefficient. Parameters ---------- n : int number of splines coef : unused for compatibility with constraints Returns ------- penalty matrix : sparse csc matrix of shape (n,n) """ return sp.sparse.eye(n).tocsc() def monotonicity_(n, coef, increasing=True): """ Builds a penalty matrix for P-Splines with continuous features. Penalizes violation of monotonicity in the feature function. Parameters ---------- n : int number of splines coef : array-like coefficients of the feature function increasing : bool, default: True whether to enforce monotic increasing, or decreasing functions Returns ------- penalty matrix : sparse csc matrix of shape (n,n) """ if n != len(coef.ravel()): raise ValueError('dimension mismatch: expected n equals len(coef), '\ 'but found n = {}, coef.shape = {}.'\ .format(n, coef.shape)) if n==1: # no monotonic penalty for constant functions return sp.sparse.csc_matrix(0.) if increasing: # only penalize the case where coef_i-1 > coef_i mask = sp.sparse.diags((np.diff(coef.ravel()) < 0).astype(float)) else: # only penalize the case where coef_i-1 < coef_i mask = sp.sparse.diags((np.diff(coef.ravel()) > 0).astype(float)) derivative = 1 D = sparse_diff(sp.sparse.identity(n).tocsc(), n=derivative) * mask return D.dot(D.T).tocsc() def monotonic_inc(n, coef): """ Builds a penalty matrix for P-Splines with continuous features. Penalizes violation of a monotonic increasing feature function. Parameters ---------- n : int number of splines coef : array-like, coefficients of the feature function Returns ------- penalty matrix : sparse csc matrix of shape (n,n) """ return monotonicity_(n, coef, increasing=True) def monotonic_dec(n, coef): """ Builds a penalty matrix for P-Splines with continuous features. Penalizes violation of a monotonic decreasing feature function. Parameters ---------- n : int number of splines coef : array-like coefficients of the feature function Returns ------- penalty matrix : sparse csc matrix of shape (n,n) """ return monotonicity_(n, coef, increasing=False) def convexity_(n, coef, convex=True): """ Builds a penalty matrix for P-Splines with continuous features. Penalizes violation of convexity in the feature function. Parameters ---------- n : int number of splines coef : array-like coefficients of the feature function convex : bool, default: True whether to enforce convex, or concave functions Returns ------- penalty matrix : sparse csc matrix of shape (n,n) """ if n != len(coef.ravel()): raise ValueError('dimension mismatch: expected n equals len(coef), '\ 'but found n = {}, coef.shape = {}.'\ .format(n, coef.shape)) if n==1: # no convex penalty for constant functions return sp.sparse.csc_matrix(0.) if convex: mask = sp.sparse.diags((np.diff(coef.ravel(), n=2) < 0).astype(float)) else: mask = sp.sparse.diags((np.diff(coef.ravel(), n=2) > 0).astype(float)) derivative = 2 D = sparse_diff(sp.sparse.identity(n).tocsc(), n=derivative) * mask return D.dot(D.T).tocsc() def convex(n, coef): """ Builds a penalty matrix for P-Splines with continuous features. Penalizes violation of a convex feature function. Parameters ---------- n : int number of splines coef : array-like coefficients of the feature function Returns ------- penalty matrix : sparse csc matrix of shape (n,n) """ return convexity_(n, coef, convex=True) def concave(n, coef): """ Builds a penalty matrix for P-Splines with continuous features. Penalizes violation of a concave feature function. Parameters ---------- n : int number of splines coef : array-like coefficients of the feature function Returns ------- penalty matrix : sparse csc matrix of shape (n,n) """ return convexity_(n, coef, convex=False) # def circular(n, coef): # """ # Builds a penalty matrix for P-Splines with continuous features. # Penalizes violation of a circular feature function. # # Parameters # ---------- # n : int # number of splines # coef : unused # for compatibility with constraints # # Returns # ------- # penalty matrix : sparse csc matrix of shape (n,n) # """ # if n != len(coef.ravel()): # raise ValueError('dimension mismatch: expected n equals len(coef), '\ # 'but found n = {}, coef.shape = {}.'\ # .format(n, coef.shape)) # # if n==1: # # no first circular penalty for constant functions # return sp.sparse.csc_matrix(0.) # # row = np.zeros(n) # row[0] = 1 # row[-1] = -1 # P = sp.sparse.vstack([row, sp.sparse.csc_matrix((n-2, n)), row[::-1]]) # return P.tocsc() def none(n, coef): """ Build a matrix of zeros for features that should go unpenalized Parameters ---------- n : int number of splines coef : unused for compatibility with constraints Returns ------- penalty matrix : sparse csc matrix of shape (n,n) """ return sp.sparse.csc_matrix(np.zeros((n, n))) def wrap_penalty(p, fit_linear, linear_penalty=0.): """ tool to account for unity penalty on the linear term of any feature. example: p = wrap_penalty(derivative, fit_linear=True)(n, coef) Parameters ---------- p : callable. penalty-matrix-generating function. fit_linear : boolean. whether the current feature has a linear term or not. linear_penalty : float, default: 0. penalty on the linear term Returns ------- wrapped_p : callable modified penalty-matrix-generating function """ def wrapped_p(n, *args): if fit_linear: if n == 1: return sp.sparse.block_diag([linear_penalty], format='csc') return sp.sparse.block_diag([linear_penalty, p(n-1, *args)], format='csc') else: return p(n, *args) return wrapped_p def sparse_diff(array, n=1, axis=-1): """ A ported sparse version of np.diff. Uses recursion to compute higher order differences Parameters ---------- array : sparse array n : int, default: 1 differencing order axis : int, default: -1 axis along which differences are computed Returns ------- diff_array : sparse array same shape as input array, but 'axis' dimension is smaller by 'n'. """ if (n < 0) or (int(n) != n): raise ValueError('Expected order is non-negative integer, '\ 'but found: {}'.format(n)) if not sp.sparse.issparse(array): warnings.warn('Array is not sparse. Consider using numpy.diff') if n == 0: return array nd = array.ndim slice1 = [slice(None)]*nd slice2 = [slice(None)]*nd slice1[axis] = slice(1, None) slice2[axis] = slice(None, -1) slice1 = tuple(slice1) slice2 = tuple(slice2) A = sparse_diff(array, n-1, axis=axis) return A[slice1] - A[slice2] PENALTIES = {'auto': 'auto', 'derivative': derivative, 'l2': l2, 'none': none, 'periodic': periodic } CONSTRAINTS = {'convex': convex, 'concave': concave, 'monotonic_inc': monotonic_inc, 'monotonic_dec': monotonic_dec, 'none': none } PKle_M--pygam/pygam.py# -*- coding: utf-8 -*- from __future__ import division, absolute_import from collections import defaultdict from collections import OrderedDict from copy import deepcopy from progressbar import ProgressBar import warnings import numpy as np import scipy as sp from scipy import stats from pygam.core import Core from pygam.penalties import derivative from pygam.penalties import l2 from pygam.penalties import monotonic_inc from pygam.penalties import monotonic_dec from pygam.penalties import convex from pygam.penalties import concave from pygam.penalties import none from pygam.penalties import wrap_penalty from pygam.penalties import PENALTIES, CONSTRAINTS from pygam.distributions import Distribution from pygam.distributions import NormalDist from pygam.distributions import BinomialDist from pygam.distributions import PoissonDist from pygam.distributions import GammaDist from pygam.distributions import InvGaussDist from pygam.distributions import DISTRIBUTIONS from pygam.links import Link from pygam.links import IdentityLink from pygam.links import LogitLink from pygam.links import LogLink from pygam.links import InverseLink from pygam.links import InvSquaredLink from pygam.links import LINKS from pygam.callbacks import CallBack from pygam.callbacks import Deviance from pygam.callbacks import Diffs from pygam.callbacks import Accuracy from pygam.callbacks import Coef from pygam.callbacks import validate_callback from pygam.callbacks import CALLBACKS from pygam.utils import check_y from pygam.utils import check_X from pygam.utils import check_X_y from pygam.utils import make_2d from pygam.utils import flatten from pygam.utils import check_array from pygam.utils import check_lengths from pygam.utils import load_diagonal from pygam.utils import TablePrinter from pygam.utils import space_row from pygam.utils import sig_code from pygam.utils import b_spline_basis from pygam.utils import combine from pygam.utils import cholesky from pygam.utils import check_param from pygam.utils import isiterable from pygam.utils import NotPositiveDefiniteError from pygam.utils import OptimizationError from pygam.terms import Term from pygam.terms import Intercept, intercept from pygam.terms import LinearTerm, l from pygam.terms import SplineTerm, s from pygam.terms import FactorTerm, f from pygam.terms import TensorTerm, te from pygam.terms import TermList from pygam.terms import MetaTermMixin EPS = np.finfo(np.float64).eps # machine epsilon class GAM(Core, MetaTermMixin): """Generalized Additive Model Parameters ---------- terms : expression specifying terms to model, optional. By default a univariate spline term will be allocated for each feature. For example: >>> GAM(s(0) + l(1) + f(2) + te(3, 4)) will fit a spline term on feature 0, a linear term on feature 1, a factor term on feature 2, and a tensor term on features 3 and 4. callbacks : list of str or list of CallBack objects, optional Names of callback objects to call during the optimization loop. distribution : str or Distribution object, optional Distribution to use in the model. link : str or Link object, optional Link function to use in the model. fit_intercept : bool, optional Specifies if a constant (a.k.a. bias or intercept) should be added to the decision function. Note: the intercept receives no smoothing penalty. max_iter : int, optional Maximum number of iterations allowed for the solver to converge. tol : float, optional Tolerance for stopping criteria. verbose : bool, optional whether to show pyGAM warnings. Attributes ---------- coef_ : array, shape (n_classes, m_features) Coefficient of the features in the decision function. If fit_intercept is True, then self.coef_[0] will contain the bias. statistics_ : dict Dictionary containing model statistics like GCV/UBRE scores, AIC/c, parameter covariances, estimated degrees of freedom, etc. logs_ : dict Dictionary containing the outputs of any callbacks at each optimization loop. The logs are structured as ``{callback: [...]}`` References ---------- Simon N. Wood, 2006 Generalized Additive Models: an introduction with R Hastie, Tibshirani, Friedman The Elements of Statistical Learning http://statweb.stanford.edu/~tibs/ElemStatLearn/printings/ESLII_print10.pdf Paul Eilers & Brian Marx, 2015 International Biometric Society: A Crash Course on P-splines http://www.ibschannel2015.nl/project/userfiles/Crash_course_handout.pdf """ def __init__(self, terms='auto', max_iter=100, tol=1e-4, distribution='normal', link='identity', callbacks=['deviance', 'diffs'], fit_intercept=True, verbose=False, **kwargs): self.max_iter = max_iter self.tol = tol self.distribution = distribution self.link = link self.callbacks = callbacks self.verbose = verbose self.terms = TermList(terms) if isinstance(terms, Term) else terms self.fit_intercept = fit_intercept for k, v in kwargs.items(): if k not in self._plural: raise TypeError('__init__() got an unexpected keyword argument {}'.format(k)) setattr(self, k, v) # internal settings self._constraint_lam = 1e9 # regularization intensity for constraints self._constraint_l2 = 1e-3 # diagononal loading to improve conditioning self._constraint_l2_max = 1e-1 # maximum loading # self._opt = 0 # use 0 for numerically stable optimizer, 1 for naive self._term_location = 'terms' # for locating sub terms # self._include = ['lam'] # call super and exclude any variables super(GAM, self).__init__() # @property # def lam(self): # if self._has_terms(): # return self.terms.lam # else: # return self._lam # # @lam.setter # def lam(self, value): # if self._has_terms(): # self.terms.lam = value # else: # self._lam = value @property def _is_fitted(self): """simple way to check if the GAM has been fitted Parameters --------- None Returns ------- bool : whether or not the model is fitted """ return hasattr(self, 'coef_') def _validate_params(self): """method to sanitize model parameters Parameters --------- None Returns ------- None """ # fit_intercep if not isinstance(self.fit_intercept, bool): raise ValueError('fit_intercept must be type bool, but found {}'\ .format(self.fit_intercept.__class__)) # terms if (self.terms is not 'auto') and not (isinstance(self.terms, (TermList, Term, type(None)))): raise ValueError('terms must be a TermList, but found '\ 'terms = {}'.format(self.terms)) # max_iter self.max_iter = check_param(self.max_iter, param_name='max_iter', dtype='int', constraint='>=1', iterable=False) # distribution if not ((self.distribution in DISTRIBUTIONS) or isinstance(self.distribution, Distribution)): raise ValueError('unsupported distribution {}'.format(self.distribution)) if self.distribution in DISTRIBUTIONS: self.distribution = DISTRIBUTIONS[self.distribution]() # link if not ((self.link in LINKS) or isinstance(self.link, Link)): raise ValueError('unsupported link {}'.format(self.link)) if self.link in LINKS: self.link = LINKS[self.link]() # callbacks if not isiterable(self.callbacks): raise ValueError('Callbacks must be iterable, but found {}'\ .format(self.callbacks)) if not all([c in CALLBACKS or isinstance(c, CallBack) for c in self.callbacks]): raise ValueError('unsupported callback(s) {}'.format(self.callbacks)) callbacks = list(self.callbacks) for i, c in enumerate(self.callbacks): if c in CALLBACKS: callbacks[i] = CALLBACKS[c]() self.callbacks = [validate_callback(c) for c in callbacks] def _validate_data_dep_params(self, X): """method to validate and prepare data-dependent parameters Parameters --------- X : array-like containing the input dataset Returns ------- None """ n_samples, m_features = X.shape # terms if self.terms is 'auto': # one numerical spline per feature self.terms = TermList(*[SplineTerm(feat, verbose=self.verbose) for feat in range(m_features)]) elif self.terms is None: # no terms self.terms = TermList() else: # user-specified self.terms = TermList(self.terms, verbose=self.verbose) # add intercept if self.fit_intercept: self.terms = self.terms + Intercept() if len(self.terms) == 0: raise ValueError('At least 1 term must be specified') # copy over things from plural remove = [] for k, v in self.__dict__.items(): if k in self._plural: setattr(self.terms, k, v) remove.append(k) for k in remove: delattr(self, k) self.terms.compile(X) def loglikelihood(self, X, y, weights=None): """ compute the log-likelihood of the dataset using the current model Parameters --------- X : array-like of shape (n_samples, m_features) containing the input dataset y : array-like of shape (n,) containing target values weights : array-like of shape (n,), optional containing sample weights Returns ------- log-likelihood : np.array of shape (n,) containing log-likelihood scores """ y = check_y(y, self.link, self.distribution, verbose=self.verbose) mu = self.predict_mu(X) if weights is not None: weights = np.array(weights).astype('f').ravel() weights = check_array(weights, name='sample weights', ndim=1, verbose=self.verbose) check_lengths(y, weights) else: weights = np.ones_like(y).astype('float64') return self._loglikelihood(y, mu, weights=weights) def _loglikelihood(self, y, mu, weights=None): """ compute the log-likelihood of the dataset using the current model Parameters --------- y : array-like of shape (n,) containing target values mu : array-like of shape (n_samples,) expected value of the targets given the model and inputs weights : array-like of shape (n,), optional containing sample weights Returns ------- log-likelihood : np.array of shape (n,) containing log-likelihood scores """ return self.distribution.log_pdf(y=y, mu=mu, weights=weights).sum() def _linear_predictor(self, X=None, modelmat=None, b=None, term=-1): """linear predictor compute the linear predictor portion of the model ie multiply the model matrix by the spline basis coefficients Parameters --------- at least 1 of (X, modelmat) and at least 1 of (b, feature) X : array-like of shape (n_samples, m_features) or None, optional containing the input dataset if None, will attempt to use modelmat modelmat : array-like or None, optional contains the spline basis for each feature evaluated at the input values for each feature, ie model matrix if None, will attempt to construct the model matrix from X b : array-like or None, optional contains the spline coefficients if None, will use current model coefficients feature : int, optional feature for which to compute the linear prediction if -1, will compute for all features Returns ------- lp : np.array of shape (n_samples,) """ if modelmat is None: modelmat = self._modelmat(X, term=term) if b is None: b = self.coef_[self.terms.get_coef_indices(term)] return modelmat.dot(b).flatten() def predict_mu(self, X): """ preduct expected value of target given model and input X Parameters --------- X : array-like of shape (n_samples, m_features), containing the input dataset Returns ------- y : np.array of shape (n_samples,) containing expected values under the model """ if not self._is_fitted: raise AttributeError('GAM has not been fitted. Call fit first.') X = check_X(X, n_feats=self.statistics_['m_features'], edge_knots=self.edge_knots_, dtypes=self.dtype, features=self.feature, verbose=self.verbose) lp = self._linear_predictor(X) return self.link.mu(lp, self.distribution) def predict(self, X): """ preduct expected value of target given model and input X often this is done via expected value of GAM given input X Parameters --------- X : array-like of shape (n_samples, m_features) containing the input dataset Returns ------- y : np.array of shape (n_samples,) containing predicted values under the model """ return self.predict_mu(X) def _modelmat(self, X, term=-1): """ Builds a model matrix, B, out of the spline basis for each feature B = [B_0, B_1, ..., B_p] Parameters --------- X : array-like of shape (n_samples, m_features) containing the input dataset term : int, optional term index for which to compute the model matrix if -1, will create the model matrix for all features Returns ------- modelmat : sparse matrix of len n_samples containing model matrix of the spline basis for selected features """ X = check_X(X, n_feats=self.statistics_['m_features'], edge_knots=self.edge_knots_, dtypes=self.dtype, features=self.feature, verbose=self.verbose) return self.terms.build_columns(X, term=term) def _cholesky(self, A, **kwargs): """ method to handle potential problems with the cholesky decomposition. will try to increase L2 regularization of the penalty matrix to do away with non-positive-definite errors Parameters ---------- A : np.array Returns ------- np.array """ # create appropriate-size diagonal matrix if sp.sparse.issparse(A): diag = sp.sparse.eye(A.shape[0]) else: diag = np.eye(A.shape[0]) constraint_l2 = self._constraint_l2 while constraint_l2 <= self._constraint_l2_max: try: L = cholesky(A, **kwargs) self._constraint_l2 = constraint_l2 return L except NotPositiveDefiniteError: if self.verbose: warnings.warn('Matrix is not positive definite. \n'\ 'Increasing l2 reg by factor of 10.', stacklevel=2) A -= constraint_l2 * diag constraint_l2 *= 10 A += constraint_l2 * diag raise NotPositiveDefiniteError('Matrix is not positive \n' 'definite.') def _P(self): """ builds the GAM block-diagonal penalty matrix in quadratic form out of penalty matrices specified for each feature. each feature penalty matrix is multiplied by a lambda for that feature. the first feature is the intercept. so for m features: P = block_diag[lam0 * P0, lam1 * P1, lam2 * P2, ... , lamm * Pm] Parameters --------- None Returns ------- P : sparse CSC matrix containing the model penalties in quadratic form """ return self.terms.build_penalties() def _C(self): """ builds the GAM block-diagonal constraint matrix in quadratic form out of constraint matrices specified for each feature. behaves like a penalty, but with a very large lambda value, ie 1e6. Parameters --------- None Returns ------- C : sparse CSC matrix containing the model constraints in quadratic form """ return self.terms.build_constraints(self.coef_, self._constraint_lam, self._constraint_l2) def _pseudo_data(self, y, lp, mu): """ compute the pseudo data for a PIRLS iterations Parameters --------- y : array-like of shape (n,) containing target data lp : array-like of shape (n,) containing linear predictions by the model mu : array-like of shape (n_samples,) expected value of the targets given the model and inputs Returns ------- pseudo_data : np.array of shape (n,) """ return lp + (y - mu) * self.link.gradient(mu, self.distribution) def _W(self, mu, weights, y=None): """ compute the PIRLS weights for model predictions. TODO lets verify the formula for this. if we use the square root of the mu with the stable opt, we get the same results as when we use non-sqrt mu with naive opt. this makes me think that they are equivalent. also, using non-sqrt mu with stable opt gives very small edofs for even lam=0.001 and the parameter variance is huge. this seems strange to me. computed [V * d(link)/d(mu)] ^(-1/2) by hand and the math checks out as hoped. ive since moved the square to the naive pirls method to make the code modular. Parameters --------- mu : array-like of shape (n_samples,) expected value of the targets given the model and inputs weights : array-like of shape (n_samples,) containing sample weights y = array-like of shape (n_samples,) or None, optional does nothing. just for compatibility with ExpectileGAM Returns ------- weights : sp..sparse array of shape (n_samples, n_samples) """ return sp.sparse.diags((self.link.gradient(mu, self.distribution)**2 * self.distribution.V(mu=mu) * weights ** -1)**-0.5) def _mask(self, weights): """ identifies the mask at which the weights are greater than sqrt(machine epsilon) and not NaN and not Inf Parameters --------- weights : array-like of shape (n,) containing weights in [0,1] Returns ------- mask : boolean np.array of shape (n,) of good weight values """ mask = (np.abs(weights) >= np.sqrt(EPS)) * np.isfinite(weights) if mask.sum() == 0: raise OptimizationError('PIRLS optimization has diverged.\n' + 'Try increasing regularization, or specifying an initial value for self.coef_') return mask def _initial_estimate(self, y, modelmat): """ Makes an inital estimate for the model coefficients. For a LinearGAM we simply initialize to small coefficients. For other GAMs we transform the problem to the linear space and solve an unpenalized version. Parameters --------- y : array-like of shape (n,) containing target data modelmat : sparse matrix of shape (n, m) containing model matrix of the spline basis Returns ------- coef : array of shape (m,) containing the initial estimate for the model coefficients Notes ----- This method implements the suggestions in Wood, section 2.2.2 Geometry and IRLS convergence, pg 80 """ # do a simple initialization for LinearGAMs if isinstance(self, LinearGAM): n, m = modelmat.shape return np.ones(m) * np.sqrt(EPS) # transform the problem to the linear scale y = deepcopy(y).astype('float64') y[y == 0] += .01 # edge case for log link, inverse link, and logit link y[y == 1] -= .01 # edge case for logit link y_ = self.link.link(y, self.distribution) y_ = make_2d(y_, verbose=False) assert np.isfinite(y_).all(), "transformed response values should be well-behaved." # solve the linear problem return np.linalg.solve(load_diagonal(modelmat.T.dot(modelmat).A), modelmat.T.dot(y_)) # not sure if this is faster... # return np.linalg.pinv(modelmat.T.dot(modelmat)).dot(modelmat.T.dot(y_)) def _pirls(self, X, Y, weights): """ Performs stable PIRLS iterations to estimate GAM coefficients Parameters --------- X : array-like of shape (n_samples, m_features) containing input data Y : array-like of shape (n,) containing target data weights : array-like of shape (n,) containing sample weights Returns ------- None """ modelmat = self._modelmat(X) # build a basis matrix for the GLM n, m = modelmat.shape # initialize GLM coefficients if model is not yet fitted if (not self._is_fitted or len(self.coef_) != self.terms.n_coefs or not np.isfinite(self.coef_).all()): # initialize the model self.coef_ = self._initial_estimate(Y, modelmat) assert np.isfinite(self.coef_).all(), "coefficients should be well-behaved, but found: {}".format(self.coef_) P = self._P() S = sp.sparse.diags(np.ones(m) * np.sqrt(EPS)) # improve condition # S += self._H # add any user-chosen minumum penalty to the diagonal # if we dont have any constraints, then do cholesky now if not self.terms.hasconstraint: E = self._cholesky(S + P, sparse=False, verbose=self.verbose) min_n_m = np.min([m,n]) Dinv = np.zeros((min_n_m + m, m)).T for _ in range(self.max_iter): # recompute cholesky if needed if self.terms.hasconstraint: P = self._P() C = self._C() E = self._cholesky(S + P + C, sparse=False, verbose=self.verbose) # forward pass y = deepcopy(Y) # for simplicity lp = self._linear_predictor(modelmat=modelmat) mu = self.link.mu(lp, self.distribution) W = self._W(mu, weights, y) # create pirls weight matrix # check for weghts == 0, nan, and update mask = self._mask(W.diagonal()) y = y[mask] # update lp = lp[mask] # update mu = mu[mask] # update W = sp.sparse.diags(W.diagonal()[mask]) # update # PIRLS Wood pg 183 pseudo_data = W.dot(self._pseudo_data(y, lp, mu)) # log on-loop-start stats self._on_loop_start(vars()) WB = W.dot(modelmat[mask,:]) # common matrix product Q, R = np.linalg.qr(WB.A) if not np.isfinite(Q).all() or not np.isfinite(R).all(): raise ValueError('QR decomposition produced NaN or Inf. '\ 'Check X data.') # need to recompute the number of singular values min_n_m = np.min([m, n, mask.sum()]) Dinv = np.zeros((m, min_n_m)) # SVD U, d, Vt = np.linalg.svd(np.vstack([R, E])) svd_mask = d <= (d.max() * np.sqrt(EPS)) # mask out small singular values np.fill_diagonal(Dinv, d**-1) # invert the singular values U1 = U[:min_n_m,:min_n_m] # keep only top corner of U # update coefficients B = Vt.T.dot(Dinv).dot(U1.T).dot(Q.T) coef_new = B.dot(pseudo_data).flatten() diff = np.linalg.norm(self.coef_ - coef_new)/np.linalg.norm(coef_new) self.coef_ = coef_new # update # log on-loop-end stats self._on_loop_end(vars()) # check convergence if diff < self.tol: break # estimate statistics even if not converged self._estimate_model_statistics(Y, modelmat, inner=None, BW=WB.T, B=B, weights=weights, U1=U1) if diff < self.tol: return print('did not converge') return # def _pirls_naive(self, X, y): # """ # Performs naive PIRLS iterations to estimate GAM coefficients # # Parameters # --------- # X : array-like of shape (n_samples, m_features) # containing input data # y : array-like of shape (n,) # containing target data # # Returns # ------- # None # """ # modelmat = self._modelmat(X) # build a basis matrix for the GLM # m = modelmat.shape[1] # # # initialize GLM coefficients # if not self._is_fitted or len(self.coef_) != sum(self._n_coeffs): # self.coef_ = np.ones(m) * np.sqrt(EPS) # allow more training # # P = self._P() # create penalty matrix # P += sp.sparse.diags(np.ones(m) * np.sqrt(EPS)) # improve condition # # for _ in range(self.max_iter): # lp = self._linear_predictor(modelmat=modelmat) # mu = self.link.mu(lp, self.distribution) # # mask = self._mask(mu) # mu = mu[mask] # update # lp = lp[mask] # update # # if self.family == 'binomial': # self.acc.append(self.accuracy(y=y[mask], mu=mu)) # log the training accuracy # self.dev.append(self.deviance_(y=y[mask], mu=mu, scaled=False)) # log the training deviance # # weights = self._W(mu)**2 # PIRLS, added square for modularity # pseudo_data = self._pseudo_data(y, lp, mu) # PIRLS # # BW = modelmat.T.dot(weights).tocsc() # common matrix product # inner = sp.sparse.linalg.inv(BW.dot(modelmat) + P) # keep for edof # # coef_new = inner.dot(BW).dot(pseudo_data).flatten() # diff = np.linalg.norm(self.coef_ - coef_new)/np.linalg.norm(coef_new) # self.diffs.append(diff) # self.coef_ = coef_new # update # # # check convergence # if diff < self.tol: # self.edof_ = self._estimate_edof(modelmat, inner, BW) # self.aic_ = self._estimate_AIC(X, y, mu) # self.aicc_ = self._estimate_AICc(X, y, mu) # return # # print('did not converge') def _on_loop_start(self, variables): """ performs on-loop-start actions like callbacks variables contains local namespace variables. Parameters --------- variables : dict of available variables Returns ------- None """ for callback in self.callbacks: if hasattr(callback, 'on_loop_start'): self.logs_[str(callback)].append(callback.on_loop_start(**variables)) def _on_loop_end(self, variables): """ performs on-loop-end actions like callbacks variables contains local namespace variables. Parameters --------- variables : dict of available variables Returns ------- None """ for callback in self.callbacks: if hasattr(callback, 'on_loop_end'): self.logs_[str(callback)].append(callback.on_loop_end(**variables)) def fit(self, X, y, weights=None): """Fit the generalized additive model. Parameters ---------- X : array-like, shape (n_samples, m_features) Training vectors. y : array-like, shape (n_samples,) Target values, ie integers in classification, real numbers in regression) weights : array-like shape (n_samples,) or None, optional Sample weights. if None, defaults to array of ones Returns ------- self : object Returns fitted GAM object """ # validate parameters self._validate_params() # validate data y = check_y(y, self.link, self.distribution, verbose=self.verbose) X = check_X(X, verbose=self.verbose) check_X_y(X, y) if weights is not None: weights = np.array(weights).astype('f').ravel() weights = check_array(weights, name='sample weights', ndim=1, verbose=self.verbose) check_lengths(y, weights) else: weights = np.ones_like(y).astype('float64') # validate data-dependent parameters self._validate_data_dep_params(X) # set up logging if not hasattr(self, 'logs_'): self.logs_ = defaultdict(list) # begin capturing statistics self.statistics_ = {} self.statistics_['n_samples'] = len(y) self.statistics_['m_features'] = X.shape[1] # optimize self._pirls(X, y, weights) # if self._opt == 0: # self._pirls(X, y, weights) # if self._opt == 1: # self._pirls_naive(X, y) return self def deviance_residuals(self, X, y, weights=None, scaled=False): """ method to compute the deviance residuals of the model these are analogous to the residuals of an OLS. Parameters ---------- X : array-like Input data array of shape (n_saples, m_features) y : array-like Output data vector of shape (n_samples,) weights : array-like shape (n_samples,) or None, optional Sample weights. if None, defaults to array of ones scaled : bool, optional whether to scale the deviance by the (estimated) distribution scale Returns ------- deviance_residuals : np.array with shape (n_samples,) """ if not self._is_fitted: raise AttributeError('GAM has not been fitted. Call fit first.') y = check_y(y, self.link, self.distribution, verbose=self.verbose) X = check_X(X, n_feats=self.statistics_['m_features'], edge_knots=self.edge_knots_, dtypes=self.dtype, features=self.feature, verbose=self.verbose) check_X_y(X, y) if weights is not None: weights = np.array(weights).astype('f').ravel() weights = check_array(weights, name='sample weights', ndim=1, verbose=self.verbose) check_lengths(y, weights) else: weights = np.ones_like(y).astype('float64') mu = self.predict_mu(X) sign = np.sign(y-mu) return sign * self.distribution.deviance(y, mu, weights=weights, scaled=scaled) ** 0.5 def _estimate_model_statistics(self, y, modelmat, inner=None, BW=None, B=None, weights=None, U1=None): """ method to compute all of the model statistics results are stored in the 'statistics_' attribute of the model, as a dictionary keyed by: - edof: estimated degrees freedom - scale: distribution scale, if applicable - cov: coefficient covariances - se: standarrd errors - AIC: Akaike Information Criterion - AICc: corrected Akaike Information Criterion - pseudo_r2: dict of Pseudo R-squared metrics - GCV: generailized cross-validation or - UBRE: Un-Biased Risk Estimator - n_samples: number of samples used in estimation Parameters ---------- y : array-like output data vector of shape (n_samples,) modelmat : array-like, default: None contains the spline basis for each feature evaluated at the input inner : array of intermediate computations from naive optimization BW : array of intermediate computations from either optimization B : array of intermediate computations from stable optimization weights : array-like shape (n_samples,) or None, default: None containing sample weights U1 : cropped U matrix from SVD. Returns ------- None """ lp = self._linear_predictor(modelmat=modelmat) mu = self.link.mu(lp, self.distribution) self.statistics_['edof_per_coef'] = np.diagonal(U1.dot(U1.T)) self.statistics_['edof'] = self.statistics_['edof_per_coef'].sum() if not self.distribution._known_scale: self.distribution.scale = self.distribution.phi(y=y, mu=mu, edof=self.statistics_['edof'], weights=weights) self.statistics_['scale'] = self.distribution.scale self.statistics_['cov'] = (B.dot(B.T)) * self.distribution.scale # parameter covariances. no need to remove a W because we are using W^2. Wood pg 184 self.statistics_['se'] = self.statistics_['cov'].diagonal()**0.5 self.statistics_['AIC'] = self._estimate_AIC(y=y, mu=mu, weights=weights) self.statistics_['AICc'] = self._estimate_AICc(y=y, mu=mu, weights=weights) self.statistics_['pseudo_r2'] = self._estimate_r2(y=y, mu=mu, weights=weights) self.statistics_['GCV'], self.statistics_['UBRE'] = self._estimate_GCV_UBRE(modelmat=modelmat, y=y, weights=weights) self.statistics_['loglikelihood'] = self._loglikelihood(y, mu, weights=weights) self.statistics_['deviance'] = self.distribution.deviance(y=y, mu=mu, weights=weights).sum() self.statistics_['p_values'] = self._estimate_p_values() def _estimate_AIC(self, y, mu, weights=None): """ estimate the Akaike Information Criterion Parameters ---------- y : array-like of shape (n_samples,) output data vector mu : array-like of shape (n_samples,), expected value of the targets given the model and inputs weights : array-like shape (n_samples,) or None, optional containing sample weights if None, defaults to array of ones Returns ------- None """ estimated_scale = not(self.distribution._known_scale) # if we estimate the scale, that adds 2 dof return -2*self._loglikelihood(y=y, mu=mu, weights=weights) + \ 2*self.statistics_['edof'] + 2*estimated_scale def _estimate_AICc(self, y, mu, weights=None): """ estimate the corrected Akaike Information Criterion relies on the estimated degrees of freedom, which must be computed before. Parameters ---------- y : array-like of shape (n_samples,) output data vector mu : array-like of shape (n_samples,) expected value of the targets given the model and inputs weights : array-like shape (n_samples,) or None, optional containing sample weights if None, defaults to array of ones Returns ------- None """ edof = self.statistics_['edof'] if self.statistics_['AIC'] is None: self.statistics_['AIC'] = self._estimate_AIC(y, mu, weights) return self.statistics_['AIC'] + 2*(edof + 1)*(edof + 2)/(y.shape[0] - edof -2) def _estimate_r2(self, X=None, y=None, mu=None, weights=None): """ estimate some pseudo R^2 values currently only computes explained deviance. results are stored Parameters ---------- y : array-like of shape (n_samples,) output data vector mu : array-like of shape (n_samples,) expected value of the targets given the model and inputs weights : array-like shape (n_samples,) or None, optional containing sample weights if None, defaults to array of ones Returns ------- None """ if mu is None: mu = self.predict_mu(X=X) if weights is None: weights = np.ones_like(y).astype('float64') null_mu = y.mean() * np.ones_like(y).astype('float64') null_d = self.distribution.deviance(y=y, mu=null_mu, weights=weights) full_d = self.distribution.deviance(y=y, mu=mu, weights=weights) null_ll = self._loglikelihood(y=y, mu=null_mu, weights=weights) full_ll = self._loglikelihood(y=y, mu=mu, weights=weights) r2 = OrderedDict() r2['explained_deviance'] = 1. - full_d.sum()/null_d.sum() r2['McFadden'] = full_ll/null_ll r2['McFadden_adj'] = 1. - (full_ll - self.statistics_['edof'])/null_ll return r2 def _estimate_GCV_UBRE(self, X=None, y=None, modelmat=None, gamma=1.4, add_scale=True, weights=None): """ Generalized Cross Validation and Un-Biased Risk Estimator. UBRE is used when the scale parameter is known, like Poisson and Binomial families. Parameters ---------- y : array-like of shape (n_samples,) output data vector modelmat : array-like, default: None contains the spline basis for each feature evaluated at the input gamma : float, default: 1.4 serves as a weighting to increase the impact of the influence matrix on the score add_scale : boolean, default: True UBRE score can be negative because the distribution scale is subtracted. to keep things positive we can add the scale back. weights : array-like shape (n_samples,) or None, default: None containing sample weights if None, defaults to array of ones Returns ------- score : float Either GCV or UBRE, depending on if the scale parameter is known. Notes ----- Sometimes the GCV or UBRE selected model is deemed to be too wiggly, and a smoother model is desired. One way to achieve this, in a systematic way, is to increase the amount that each model effective degree of freedom counts, in the GCV or UBRE score, by a factor γ ≥ 1 see Wood 2006 pg. 177-182, 220 for more details. """ if gamma < 1: raise ValueError('gamma scaling should be greater than 1, '\ 'but found gamma = {}',format(gamma)) if modelmat is None: modelmat = self._modelmat(X) if weights is None: weights = np.ones_like(y).astype('float64') lp = self._linear_predictor(modelmat=modelmat) mu = self.link.mu(lp, self.distribution) n = y.shape[0] edof = self.statistics_['edof'] GCV = None UBRE = None dev = self.distribution.deviance(mu=mu, y=y, scaled=False, weights=weights).sum() if self.distribution._known_scale: # scale is known, use UBRE scale = self.distribution.scale UBRE = 1./n * dev - (~add_scale)*(scale) + 2.*gamma/n * edof * scale else: # scale unkown, use GCV GCV = (n * dev) / (n - gamma * edof)**2 return (GCV, UBRE) def _estimate_p_values(self): """estimate the p-values for all features """ if not self._is_fitted: raise AttributeError('GAM has not been fitted. Call fit first.') p_values = [] for term_i in range(len(self.terms)): p_values.append(self._compute_p_value(term_i)) return p_values def _compute_p_value(self, term_i): """compute the p-value of the desired feature Arguments --------- term_i : int term to select from the data Returns ------- p_value : float Notes ----- Wood 2006, section 4.8.5: The p-values, calculated in this manner, behave correctly for un-penalized models, or models with known smoothing parameters, but when smoothing parameters have been estimated, the p-values are typically lower than they should be, meaning that the tests reject the null too readily. (...) In practical terms, if these p-values suggest that a term is not needed in a model, then this is probably true, but if a term is deemed ‘significant’ it is important to be aware that this significance may be overstated. based on equations from Wood 2006 section 4.8.5 page 191 and errata https://people.maths.bris.ac.uk/~sw15190/igam/iGAMerrata-12.pdf the errata shows a correction for the f-statisitc. """ if not self._is_fitted: raise AttributeError('GAM has not been fitted. Call fit first.') idxs = self.terms.get_coef_indices(term_i) cov = self.statistics_['cov'][idxs][:, idxs] coef = self.coef_[idxs] # center non-intercept term functions if isinstance(self.terms[term_i], SplineTerm): coef -= coef.mean() inv_cov, rank = sp.linalg.pinv(cov, return_rank=True) score = coef.T.dot(inv_cov).dot(coef) # compute p-values if self.distribution._known_scale: # for known scale use chi-squared statistic return 1 - sp.stats.chi2.cdf(x=score, df=rank) else: # if scale has been estimated, prefer to use f-statisitc score = score / rank return 1 - sp.stats.f.cdf(score, rank, self.statistics_['n_samples'] - self.statistics_['edof']) def confidence_intervals(self, X, width=.95, quantiles=None): """estimate confidence intervals for the model. Parameters ---------- X : array-like of shape (n_samples, m_features) Input data matrix width : float on [0,1], optional quantiles : array-like of floats in (0, 1), optional Instead of specifying the prediciton width, one can specify the quantiles. So ``width=.95`` is equivalent to ``quantiles=[.025, .975]`` Returns ------- intervals: np.array of shape (n_samples, 2 or len(quantiles)) Notes ----- Wood 2006, section 4.9 Confidence intervals based on section 4.8 rely on large sample results to deal with non-Gaussian distributions, and treat the smoothing parameters as fixed, when in reality they are estimated from the data. """ if not self._is_fitted: raise AttributeError('GAM has not been fitted. Call fit first.') X = check_X(X, n_feats=self.statistics_['m_features'], edge_knots=self.edge_knots_, dtypes=self.dtype, features=self.feature, verbose=self.verbose) return self._get_quantiles(X, width, quantiles, prediction=False) def _get_quantiles(self, X, width, quantiles, modelmat=None, lp=None, prediction=False, xform=True, term=-1): """ estimate prediction intervals for LinearGAM Parameters ---------- X : array input data of shape (n_samples, m_features) width : float on (0, 1) quantiles : array-like of floats on (0, 1) instead of specifying the prediciton width, one can specify the quantiles. so width=.95 is equivalent to quantiles=[.025, .975] modelmat : array of shape or None, default: None lp : array or None, default: None prediction : bool, default: True. whether to compute prediction intervals (True) or confidence intervals (False) xform : bool, default: True, whether to apply the inverse link function and return values on the scale of the distribution mean (True), or to keep on the linear predictor scale (False) term : int, default: -1 Returns ------- intervals: np.array of shape (n_samples, 2 or len(quantiles)) Notes ----- when the scale parameter is known, then we can proceed with a large sample approximation to the distribution of the model coefficients where B_hat ~ Normal(B, cov) when the scale parameter is unknown, then we have to account for the distribution of the estimated scale parameter, which is Chi-squared. since we scale our estimate of B_hat by the sqrt of estimated scale, we get a t distribution: Normal / sqrt(Chi-squared) ~ t see Simon Wood section 1.3.2, 1.3.3, 1.5.5, 2.1.5 """ if quantiles is not None: quantiles = np.atleast_1d(quantiles) else: alpha = (1 - width)/2. quantiles = [alpha, 1 - alpha] for quantile in quantiles: if (quantile >= 1) or (quantile <= 0): raise ValueError('quantiles must be in (0, 1), but found {}'\ .format(quantiles)) if modelmat is None: modelmat = self._modelmat(X, term=term) if lp is None: lp = self._linear_predictor(modelmat=modelmat, term=term) idxs = self.terms.get_coef_indices(term) cov = self.statistics_['cov'][idxs][:, idxs] var = (modelmat.dot(cov) * modelmat.A).sum(axis=1) if prediction: var += self.distribution.scale lines = [] for quantile in quantiles: if self.distribution._known_scale: q = sp.stats.norm.ppf(quantile) else: q = sp.stats.t.ppf(quantile, df=self.statistics_['n_samples'] - self.statistics_['edof']) lines.append(lp + q * var**0.5) lines = np.vstack(lines).T if xform: lines = self.link.mu(lines, self.distribution) return lines def _flatten_mesh(self, Xs, term): """flatten the mesh and distribute into a feature matrix""" n = Xs[0].size if self.terms[term].istensor: terms = self.terms[term] else: terms = [self.terms[term]] X = np.zeros((n, self.statistics_['m_features'])) for term_, x in zip(terms, Xs): X[:, term_.feature] = x.ravel() return X def generate_X_grid(self, term, n=100, meshgrid=False): """create a nice grid of X data array is sorted by feature and uniformly spaced, so the marginal and joint distributions are likely wrong if term is >= 0, we generate n samples per feature, which results in n^deg samples, where deg is the degree of the interaction of the term Parameters ---------- term : int, Which term to process. n : int, optional number of data points to create meshgrid : bool, optional Whether to return a meshgrid (useful for 3d plotting) or a feature matrix (useful for inference like partial predictions) Returns ------- if meshgrid is False: np.array of shape (n, n_features) where m is the number of (sub)terms in the requested (tensor)term. else: tuple of len m, where m is the number of (sub)terms in the requested (tensor)term. each element in the tuple contains a np.ndarray of size (n)^m Raises ------ ValueError : If the term requested is an intercept since it does not make sense to process the intercept term. """ if not self._is_fitted: raise AttributeError('GAM has not been fitted. Call fit first.') # cant do Intercept if self.terms[term].isintercept: raise ValueError('cannot create grid for intercept term') # process each subterm in a TensorTerm if self.terms[term].istensor: Xs = [] for term_ in self.terms[term]: Xs.append(np.linspace(term_.edge_knots_[0], term_.edge_knots_[1], num=n)) Xs = np.meshgrid(*Xs, indexing='ij') if meshgrid: return tuple(Xs) else: return self._flatten_mesh(Xs, term=term) # all other Terms elif hasattr(self.terms[term], 'edge_knots_'): x = np.linspace(self.terms[term].edge_knots_[0], self.terms[term].edge_knots_[1], num=n) if meshgrid: return (x,) # fill in feature matrix with only relevant features for this term X = np.zeros((n, self.statistics_['m_features'])) X[:, self.terms[term].feature] = x if getattr(self.terms[term], 'by', None) is not None: X[:, self.terms[term].by] = 1. return X # dont know what to do here else: raise TypeError('Unexpected term type: {}'.format(self.terms[term])) def partial_dependence(self, term, X=None, width=None, quantiles=None, meshgrid=False): """ Computes the term functions for the GAM and possibly their confidence intervals. if both width=None and quantiles=None, then no confidence intervals are computed Parameters ---------- term : int, optional Term for which to compute the partial dependence functions. X : array-like with input data, optional if `meshgrid=False`, then `X` should be an array-like of shape (n_samples, m_features). if `meshgrid=True`, then `X` should be a tuple containing an array for each feature in the term. if None, an equally spaced grid of points is generated. width : float on (0, 1), optional Width of the confidence interval. quantiles : array-like of floats on (0, 1), optional instead of specifying the prediciton width, one can specify the quantiles. so width=.95 is equivalent to quantiles=[.025, .975]. if None, defaults to width. meshgrid : bool, whether to return and accept meshgrids. Useful for creating outputs that are suitable for 3D plotting. Note, for simple terms with no interactions, the output of this function will be the same for ``meshgrid=True`` and ``meshgrid=False``, but the inputs will need to be different. Returns ------- pdeps : np.array of shape (n_samples,) conf_intervals : list of length len(term) containing np.arrays of shape (n_samples, 2 or len(quantiles)) Raises ------ ValueError : If the term requested is an intercept since it does not make sense to process the intercept term. See Also -------- generate_X_grid : for help creating meshgrids. """ if not self._is_fitted: raise AttributeError('GAM has not been fitted. Call fit first.') if not isinstance(term, int): raise ValueError('term must be an integer, but found term: {}'.format(term)) # ensure term exists if (term >= len(self.terms)) or (term < -1): raise ValueError('Term {} out of range for model with {} terms'\ .format(term, len(self.terms))) # cant do Intercept if self.terms[term].isintercept: raise ValueError('cannot create grid for intercept term') if X is None: X = self.generate_X_grid(term=term, meshgrid=meshgrid) if meshgrid: if not isinstance(X, tuple): raise ValueError('X must be a tuple of grids if `meshgrid=True`, '\ 'but found X: {}'.format(X)) shape = X[0].shape X = self._flatten_mesh(X, term=term) X = check_X(X, n_feats=self.statistics_['m_features'], edge_knots=self.edge_knots_, dtypes=self.dtype, features=self.feature, verbose=self.verbose) modelmat = self._modelmat(X, term=term) pdep = self._linear_predictor(modelmat=modelmat, term=term) out = [pdep] compute_quantiles = (width is not None) or (quantiles is not None) if compute_quantiles: conf_intervals = self._get_quantiles(X, width=width, quantiles=quantiles, modelmat=modelmat, lp=pdep, term=term, xform=False) out += [conf_intervals] if meshgrid: for i, array in enumerate(out): # add extra dimensions arising from multiple confidence intervals if array.ndim > 1: depth = array.shape[-1] shape += (depth,) out[i] = np.reshape(array, shape) if compute_quantiles: return out return out[0] def summary(self): """produce a summary of the model statistics Parameters ---------- None Returns ------- None """ if not self._is_fitted: raise AttributeError('GAM has not been fitted. Call fit first.') # high-level model summary width_details = 47 width_results = 58 model_fmt = [ (self.__class__.__name__, 'model_details', width_details), ('', 'model_results', width_results) ] model_details = [] objective = 'UBRE' if self.distribution._known_scale else 'GCV' model_details.append({'model_details': space_row('Distribution:', self.distribution.__class__.__name__, total_width=width_details), 'model_results': space_row('Effective DoF:', str(np.round(self.statistics_['edof'], 4)), total_width=width_results)}) model_details.append({'model_details': space_row('Link Function:', self.link.__class__.__name__, total_width=width_details), 'model_results': space_row('Log Likelihood:', str(np.round(self.statistics_['loglikelihood'], 4)), total_width=width_results)}) model_details.append({'model_details': space_row('Number of Samples:', str(self.statistics_['n_samples']), total_width=width_details), 'model_results': space_row('AIC: ', str(np.round(self.statistics_['AIC'], 4)), total_width=width_results)}) model_details.append({'model_results': space_row('AICc: ', str(np.round(self.statistics_['AICc'], 4)), total_width=width_results)}) model_details.append({'model_results': space_row(objective + ':', str(np.round(self.statistics_[objective], 4)), total_width=width_results)}) model_details.append({'model_results': space_row('Scale:', str(np.round(self.statistics_['scale'], 4)), total_width=width_results)}) model_details.append({'model_results': space_row('Pseudo R-Squared:', str(np.round(self.statistics_['pseudo_r2']['explained_deviance'], 4)), total_width=width_results)}) # term summary data = [] for i, term in enumerate(self.terms): # TODO bug: if the number of samples is less than the number of coefficients # we cant get the edof per term if len(self.statistics_['edof_per_coef']) == len(self.coef_): idx = self.terms.get_coef_indices(i) edof = np.round(self.statistics_['edof_per_coef'][idx].sum(), 1) else: edof = '' term_data = { 'feature_func': repr(term), 'lam': '' if term.isintercept else np.round(flatten(term.lam), 4), 'rank': '{}'.format(term.n_coefs), 'edof': '{}'.format(edof), 'p_value': '%.2e'%(self.statistics_['p_values'][i]), 'sig_code': sig_code(self.statistics_['p_values'][i]) } data.append(term_data) fmt = [ ('Feature Function', 'feature_func', 33), ('Lambda', 'lam', 20), ('Rank', 'rank', 12), ('EDoF', 'edof', 12), ('P > x', 'p_value', 12), ('Sig. Code', 'sig_code', 12) ] print( TablePrinter(model_fmt, ul='=', sep=' ')(model_details) ) print("="*106) print( TablePrinter(fmt, ul='=')(data) ) print("="*106) print("Significance codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1") print() print("WARNING: Fitting splines and a linear function to a feature introduces a model identifiability problem\n" \ " which can cause p-values to appear significant when they are not.") print() print("WARNING: p-values calculated in this manner behave correctly for un-penalized models or models with\n" \ " known smoothing parameters, but when smoothing parameters have been estimated, the p-values\n" \ " are typically lower than they should be, meaning that the tests reject the null too readily.") # P-VALUE BUG warnings.warn("KNOWN BUG: p-values computed in this summary are likely "\ "much smaller than they should be. \n \n"\ "Please do not make inferences based on these values! \n\n"\ "Collaborate on a solution, and stay up to date at: \n"\ "github.com/dswah/pyGAM/issues/163 \n", stacklevel=2) def gridsearch(self, X, y, weights=None, return_scores=False, keep_best=True, objective='auto', progress=True, **param_grids): """ Performs a grid search over a space of parameters for a given objective Warnings -------- ``gridsearch`` is lazy and will not remove useless combinations from the search space, eg. >>> n_splines=np.arange(5,10), fit_splines=[True, False] will result in 10 loops, of which 5 are equivalent because ``fit_splines = False`` Also, it is not recommended to search over a grid that alternates between known scales and unknown scales, as the scores of the candidate models will not be comparable. Parameters ---------- X : array-like input data of shape (n_samples, m_features) y : array-like label data of shape (n_samples,) weights : array-like shape (n_samples,), optional sample weights return_scores : boolean, optional whether to return the hyperpamaters and score for each element in the grid keep_best : boolean, optional whether to keep the best GAM as self. objective : {'auto', 'AIC', 'AICc', 'GCV', 'UBRE'}, optional Metric to optimize. If `auto`, then grid search will optimize `GCV` for models with unknown scale and `UBRE` for models with known scale. progress : bool, optional whether to display a progress bar **kwargs pairs of parameters and iterables of floats, or parameters and iterables of iterables of floats. If no parameter are specified, ``lam=np.logspace(-3, 3, 11)`` is used. This results in a 11 points, placed diagonally across lam space. If grid is iterable of iterables of floats, the outer iterable must have length ``m_features``. the cartesian product of the subgrids in the grid will be tested. If grid is a 2d numpy array, each row of the array will be tested. The method will make a grid of all the combinations of the parameters and fit a GAM to each combination. Returns ------- if ``return_scores=True``: model_scores: dict containing each fitted model as keys and corresponding objective scores as values else: self: ie possibly the newly fitted model Examples -------- For a model with 4 terms, and where we expect 4 lam values, our search space for lam must have 4 dimensions. We can search the space in 3 ways: 1. via cartesian product by specifying the grid as a list. our grid search will consider ``11 ** 4`` points: >>> lam = np.logspace(-3, 3, 11) >>> lams = [lam] * 4 >>> gam.gridsearch(X, y, lam=lams) 2. directly by specifying the grid as a np.ndarray. This is useful for when the dimensionality of the search space is very large, and we would prefer to execute a randomized search: >>> lams = np.exp(np.random.random(50, 4) * 6 - 3) >>> gam.gridsearch(X, y, lam=lams) 3. copying grids for parameters with multiple dimensions. if we specify a 1D np.ndarray for lam, we are implicitly testing the space where all points have the same value >>> gam.gridsearch(lam=np.logspace(-3, 3, 11)) is equivalent to: >>> lam = np.logspace(-3, 3, 11) >>> lams = np.array([lam] * 4) >>> gam.gridsearch(X, y, lam=lams) """ # check if model fitted if not self._is_fitted: self._validate_params() self._validate_data_dep_params(X) y = check_y(y, self.link, self.distribution, verbose=self.verbose) X = check_X(X, verbose=self.verbose) check_X_y(X, y) if weights is not None: weights = np.array(weights).astype('f').ravel() weights = check_array(weights, name='sample weights', ndim=1, verbose=self.verbose) check_lengths(y, weights) else: weights = np.ones_like(y).astype('float64') # validate objective if objective not in ['auto', 'GCV', 'UBRE', 'AIC', 'AICc']: raise ValueError("objective mut be in "\ "['auto', 'GCV', 'UBRE', 'AIC', 'AICc'], '\ 'but found objective = {}".format(objective)) # check objective if self.distribution._known_scale: if objective == 'GCV': raise ValueError('GCV should be used for models with'\ 'unknown scale') if objective == 'auto': objective = 'UBRE' else: if objective == 'UBRE': raise ValueError('UBRE should be used for models with '\ 'known scale') if objective == 'auto': objective = 'GCV' # if no params, then set up default gridsearch if not bool(param_grids): param_grids['lam'] = np.logspace(-3, 3, 11) # validate params admissible_params = list(self.get_params()) + self._plural params = [] grids = [] for param, grid in list(param_grids.items()): # check param exists if param not in (admissible_params): raise ValueError('unknown parameter: {}'.format(param)) # check grid is iterable at all if not (isiterable(grid) and (len(grid) > 1)): \ raise ValueError('{} grid must either be iterable of ' 'iterables, or an iterable of lengnth > 1, '\ 'but found {}'.format(param, grid)) # prepare grid if any(isiterable(g) for g in grid): # get required parameter shape target_len = len(flatten(getattr(self, param))) # check if cartesian product needed cartesian = (not isinstance(grid, np.ndarray) or grid.ndim != 2) # build grid grid = [np.atleast_1d(g) for g in grid] # check chape msg = '{} grid should have {} columns, '\ 'but found grid with {} columns'.format(param, target_len, len(grid)) if cartesian: if len(grid) != target_len: raise ValueError(msg) grid = combine(*grid) if not all([len(subgrid) == target_len for subgrid in grid]): raise ValueError(msg) # save param name and grid params.append(param) grids.append(grid) # build a list of dicts of candidate model params param_grid_list = [] for candidate in combine(*grids): param_grid_list.append(dict(zip(params,candidate))) # set up data collection best_model = None # keep the best model best_score = np.inf scores = [] models = [] # check if our model has been fitted already and store it if self._is_fitted: models.append(self) scores.append(self.statistics_[objective]) # our model is currently the best best_model = models[-1] best_score = scores[-1] # make progressbar optional if progress: pbar = ProgressBar() else: pbar = lambda x: x # loop through candidate model params for param_grid in pbar(param_grid_list): try: # try fitting # define new model gam = deepcopy(self) gam.set_params(self.get_params()) gam.set_params(**param_grid) # warm start with parameters from previous build if models: coef = models[-1].coef_ gam.set_params(coef_=coef, force=True, verbose=False) gam.fit(X, y, weights) except ValueError as error: msg = str(error) + '\non model with params:\n' + str(param_grid) msg += '\nskipping...\n' if self.verbose: warnings.warn(msg) continue # record results models.append(gam) scores.append(gam.statistics_[objective]) # track best if scores[-1] < best_score: best_model = models[-1] best_score = scores[-1] # problems if len(models) == 0: msg = 'No models were fitted.' if self.verbose: warnings.warn(msg) return self # copy over the best if keep_best: self.set_params(deep=True, force=True, **best_model.get_params(deep=True)) if return_scores: return OrderedDict(zip(models, scores)) else: return self def sample(self, X, y, quantity='y', sample_at_X=None, weights=None, n_draws=100, n_bootstraps=5, objective='auto'): """Simulate from the posterior of the coefficients and smoothing params. Samples are drawn from the posterior of the coefficients and smoothing parameters given the response in an approximate way. The GAM must already be fitted before calling this method; if the model has not been fitted, then an exception is raised. Moreover, it is recommended that the model and its hyperparameters be chosen with `gridsearch` (with the parameter `keep_best=True`) before calling `sample`, so that the result of that gridsearch can be used to generate useful response data and so that the model's coefficients (and their covariance matrix) can be used as the first bootstrap sample. These samples are drawn as follows. Details are in the reference below. 1. ``n_bootstraps`` many "bootstrap samples" of the response (``y``) are simulated by drawing random samples from the model's distribution evaluated at the expected values (``mu``) for each sample in ``X``. 2. A copy of the model is fitted to each of those bootstrap samples of the response. The result is an approximation of the distribution over the smoothing parameter ``lam`` given the response data ``y``. 3. Samples of the coefficients are simulated from a multivariate normal using the bootstrap samples of the coefficients and their covariance matrices. Notes ----- A ``gridsearch`` is done ``n_bootstraps`` many times, so keep ``n_bootstraps`` small. Make ``n_bootstraps < n_draws`` to take advantage of the expensive bootstrap samples of the smoothing parameters. Parameters ----------- X : array of shape (n_samples, m_features) empirical input data y : array of shape (n_samples,) empirical response vector quantity : {'y', 'coef', 'mu'}, default: 'y' What quantity to return pseudorandom samples of. If `sample_at_X` is not None and `quantity` is either `'y'` or `'mu'`, then samples are drawn at the values of `X` specified in `sample_at_X`. sample_at_X : array of shape (n_samples_to_simulate, m_features) or None, optional Input data at which to draw new samples. Only applies for `quantity` equal to `'y'` or to `'mu`'. If `None`, then `sample_at_X` is replaced by `X`. weights : np.array of shape (n_samples,) sample weights n_draws : positive int, optional (default=100) The number of samples to draw from the posterior distribution of the coefficients and smoothing parameters n_bootstraps : positive int, optional (default=5) The number of bootstrap samples to draw from simulations of the response (from the already fitted model) to estimate the distribution of the smoothing parameters given the response data. If `n_bootstraps` is 1, then only the already fitted model's smoothing parameter is used, and the distribution over the smoothing parameters is not estimated using bootstrap sampling. objective : string, optional (default='auto' metric to optimize in grid search. must be in ['AIC', 'AICc', 'GCV', 'UBRE', 'auto'] if 'auto', then grid search will optimize GCV for models with unknown scale and UBRE for models with known scale. Returns ------- draws : 2D array of length n_draws Simulations of the given `quantity` using samples from the posterior distribution of the coefficients and smoothing parameter given the response data. Each row is a pseudorandom sample. If `quantity == 'coef'`, then the number of columns of `draws` is the number of coefficients (`len(self.coef_)`). Otherwise, the number of columns of `draws` is the number of rows of `sample_at_X` if `sample_at_X` is not `None` or else the number of rows of `X`. References ---------- Simon N. Wood, 2006. Generalized Additive Models: an introduction with R. Section 4.9.3 (pages 198–199) and Section 5.4.2 (page 256–257). """ if quantity not in {'mu', 'coef', 'y'}: raise ValueError("`quantity` must be one of 'mu', 'coef', 'y';" " got {}".format(quantity)) coef_draws = self._sample_coef( X, y, weights=weights, n_draws=n_draws, n_bootstraps=n_bootstraps, objective=objective) if quantity == 'coef': return coef_draws if sample_at_X is None: sample_at_X = X linear_predictor = self._modelmat(sample_at_X).dot(coef_draws.T) mu_shape_n_draws_by_n_samples = self.link.mu( linear_predictor, self.distribution).T if quantity == 'mu': return mu_shape_n_draws_by_n_samples else: return self.distribution.sample(mu_shape_n_draws_by_n_samples) def _sample_coef(self, X, y, weights=None, n_draws=100, n_bootstraps=1, objective='auto'): """Simulate from the posterior of the coefficients. NOTE: A `gridsearch` is done `n_bootstraps` many times, so keep `n_bootstraps` small. Make `n_bootstraps < n_draws` to take advantage of the expensive bootstrap samples of the smoothing parameters. Parameters ----------- X : array of shape (n_samples, m_features) input data y : array of shape (n_samples,) response vector weights : np.array of shape (n_samples,) sample weights n_draws : positive int, optional (default=100 The number of samples to draw from the posterior distribution of the coefficients and smoothing parameters n_bootstraps : positive int, optional (default=1 The number of bootstrap samples to draw from simulations of the response (from the already fitted model) to estimate the distribution of the smoothing parameters given the response data. If `n_bootstraps` is 1, then only the already fitted model's smoothing parameters is used. objective : string, optional (default='auto' metric to optimize in grid search. must be in ['AIC', 'AICc', 'GCV', 'UBRE', 'auto'] if 'auto', then grid search will optimize GCV for models with unknown scale and UBRE for models with known scale. Returns ------- coef_samples : array of shape (n_draws, n_samples) Approximate simulations of the coefficients drawn from the posterior distribution of the coefficients and smoothing parameters given the response data References ---------- Simon N. Wood, 2006. Generalized Additive Models: an introduction with R. Section 4.9.3 (pages 198–199) and Section 5.4.2 (page 256–257). """ if not self._is_fitted: raise AttributeError('GAM has not been fitted. Call fit first.') if n_bootstraps < 1: raise ValueError('n_bootstraps must be >= 1;' ' got {}'.format(n_bootstraps)) if n_draws < 1: raise ValueError('n_draws must be >= 1;' ' got {}'.format(n_draws)) coef_bootstraps, cov_bootstraps = ( self._bootstrap_samples_of_smoothing(X, y, weights=weights, n_bootstraps=n_bootstraps, objective=objective)) coef_draws = self._simulate_coef_from_bootstraps( n_draws, coef_bootstraps, cov_bootstraps) return coef_draws def _bootstrap_samples_of_smoothing(self, X, y, weights=None, n_bootstraps=1, objective='auto'): """Sample the smoothing parameters using simulated response data. For now, the grid of `lam` values is 11 random points in M-dimensional space, where M = the number of lam values, ie len(flatten(gam.lam)) all values are in [1e-3, 1e3] """ mu = self.predict_mu(X) # Wood pg. 198 step 1 coef_bootstraps = [self.coef_] cov_bootstraps = [ load_diagonal(self.statistics_['cov'])] for _ in range(n_bootstraps - 1): # Wood pg. 198 step 2 # generate response data from fitted model (Wood pg. 198 step 3) y_bootstrap = self.distribution.sample(mu) # fit smoothing parameters on the bootstrap data # (Wood pg. 198 step 4) # TODO: Either enable randomized searches over hyperparameters # (like in sklearn's RandomizedSearchCV), or draw enough samples of # `lam` so that each of these bootstrap samples get different # values of `lam`. Right now, each bootstrap sample uses the exact # same grid of values for `lam`, so it is not worth setting # `n_bootstraps > 1`. gam = deepcopy(self) gam.set_params(self.get_params()) # create a random search of 11 points in lam space # with all values in [1e-3, 1e3] lam_grid = np.random.randn(11, len(flatten(self.lam))) * 6 - 3 lam_grid = np.exp(lam_grid) gam.gridsearch(X, y_bootstrap, weights=weights, lam=lam_grid, objective=objective) lam = gam.lam # fit coefficients on the original data given the smoothing params # (Wood pg. 199 step 5) gam = deepcopy(self) gam.set_params(self.get_params()) gam.lam = lam gam.fit(X, y, weights=weights) coef_bootstraps.append(gam.coef_) cov = load_diagonal(gam.statistics_['cov']) cov_bootstraps.append(cov) return coef_bootstraps, cov_bootstraps def _simulate_coef_from_bootstraps( self, n_draws, coef_bootstraps, cov_bootstraps): """Simulate coefficients using bootstrap samples.""" # Sample indices uniformly from {0, ..., n_bootstraps - 1} # (Wood pg. 199 step 6) random_bootstrap_indices = np.random.choice( np.arange(len(coef_bootstraps)), size=n_draws, replace=True) # Simulate `n_draws` many random coefficient vectors from a # multivariate normal distribution with mean and covariance given by # the bootstrap samples (indexed by `random_bootstrap_indices`) of # `coef_bootstraps` and `cov_bootstraps`. Because it's faster to draw # many samples from a certain distribution all at once, we make a dict # mapping bootstrap indices to draw indices and use the `size` # parameter of `np.random.multivariate_normal` to sample the draws # needed from that bootstrap sample all at once. bootstrap_index_to_draw_indices = defaultdict(list) for draw_index, bootstrap_index in enumerate(random_bootstrap_indices): bootstrap_index_to_draw_indices[bootstrap_index].append(draw_index) coef_draws = np.empty((n_draws, len(self.coef_))) for bootstrap, draw_indices in bootstrap_index_to_draw_indices.items(): coef_draws[draw_indices] = np.random.multivariate_normal( coef_bootstraps[bootstrap], cov_bootstraps[bootstrap], size=len(draw_indices)) return coef_draws class LinearGAM(GAM): """Linear GAM This is a GAM with a Normal error distribution, and an identity link. Parameters ---------- terms : expression specifying terms to model, optional. By default a univariate spline term will be allocated for each feature. For example: >>> GAM(s(0) + l(1) + f(2) + te(3, 4)) will fit a spline term on feature 0, a linear term on feature 1, a factor term on feature 2, and a tensor term on features 3 and 4. callbacks : list of str or list of CallBack objects, optional Names of callback objects to call during the optimization loop. fit_intercept : bool, optional Specifies if a constant (a.k.a. bias or intercept) should be added to the decision function. Note: the intercept receives no smoothing penalty. max_iter : int, optional Maximum number of iterations allowed for the solver to converge. tol : float, optional Tolerance for stopping criteria. verbose : bool, optional whether to show pyGAM warnings. Attributes ---------- coef_ : array, shape (n_classes, m_features) Coefficient of the features in the decision function. If fit_intercept is True, then self.coef_[0] will contain the bias. statistics_ : dict Dictionary containing model statistics like GCV/UBRE scores, AIC/c, parameter covariances, estimated degrees of freedom, etc. logs_ : dict Dictionary containing the outputs of any callbacks at each optimization loop. The logs are structured as ``{callback: [...]}`` References ---------- Simon N. Wood, 2006 Generalized Additive Models: an introduction with R Hastie, Tibshirani, Friedman The Elements of Statistical Learning http://statweb.stanford.edu/~tibs/ElemStatLearn/printings/ESLII_print10.pdf Paul Eilers & Brian Marx, 2015 International Biometric Society: A Crash Course on P-splines http://www.ibschannel2015.nl/project/userfiles/Crash_course_handout.pdf """ def __init__(self, terms='auto', max_iter=100, tol=1e-4, scale=None, callbacks=['deviance', 'diffs'], fit_intercept=True, verbose=False, **kwargs): self.scale = scale super(LinearGAM, self).__init__(terms=terms, distribution=NormalDist(scale=self.scale), link='identity', max_iter=max_iter, tol=tol, fit_intercept=fit_intercept, verbose=verbose, **kwargs) self._exclude += ['distribution', 'link'] def _validate_params(self): """ method to sanitize model parameters Parameters --------- None Returns ------- None """ self.distribution = NormalDist(scale=self.scale) super(LinearGAM, self)._validate_params() def prediction_intervals(self, X, width=.95, quantiles=None): """ estimate prediction intervals for LinearGAM Parameters ---------- X : array-like of shape (n_samples, m_features) input data matrix width : float on [0,1], optional (default=0.95 quantiles : array-like of floats in [0, 1], default: None) instead of specifying the prediciton width, one can specify the quantiles. so width=.95 is equivalent to quantiles=[.025, .975] Returns ------- intervals: np.array of shape (n_samples, 2 or len(quantiles)) """ if not self._is_fitted: raise AttributeError('GAM has not been fitted. Call fit first.') X = check_X(X, n_feats=self.statistics_['m_features'], edge_knots=self.edge_knots_, dtypes=self.dtype, features=self.feature, verbose=self.verbose) return self._get_quantiles(X, width, quantiles, prediction=True) class LogisticGAM(GAM): """Logistic GAM This is a GAM with a Binomial error distribution, and a logit link. Parameters ---------- terms : expression specifying terms to model, optional. By default a univariate spline term will be allocated for each feature. For example: >>> GAM(s(0) + l(1) + f(2) + te(3, 4)) will fit a spline term on feature 0, a linear term on feature 1, a factor term on feature 2, and a tensor term on features 3 and 4. callbacks : list of str or list of CallBack objects, optional Names of callback objects to call during the optimization loop. fit_intercept : bool, optional Specifies if a constant (a.k.a. bias or intercept) should be added to the decision function. Note: the intercept receives no smoothing penalty. max_iter : int, optional Maximum number of iterations allowed for the solver to converge. tol : float, optional Tolerance for stopping criteria. verbose : bool, optional whether to show pyGAM warnings. Attributes ---------- coef_ : array, shape (n_classes, m_features) Coefficient of the features in the decision function. If fit_intercept is True, then self.coef_[0] will contain the bias. statistics_ : dict Dictionary containing model statistics like GCV/UBRE scores, AIC/c, parameter covariances, estimated degrees of freedom, etc. logs_ : dict Dictionary containing the outputs of any callbacks at each optimization loop. The logs are structured as ``{callback: [...]}`` References ---------- Simon N. Wood, 2006 Generalized Additive Models: an introduction with R Hastie, Tibshirani, Friedman The Elements of Statistical Learning http://statweb.stanford.edu/~tibs/ElemStatLearn/printings/ESLII_print10.pdf Paul Eilers & Brian Marx, 2015 International Biometric Society: A Crash Course on P-splines http://www.ibschannel2015.nl/project/userfiles/Crash_course_handout.pdf """ def __init__(self, terms='auto', max_iter=100, tol=1e-4, callbacks=['deviance', 'diffs', 'accuracy'], fit_intercept=True, verbose=False, **kwargs): # call super super(LogisticGAM, self).__init__(terms=terms, distribution='binomial', link='logit', max_iter=max_iter, tol=tol, callbacks=callbacks, fit_intercept=fit_intercept, verbose=verbose, **kwargs) # ignore any variables self._exclude += ['distribution', 'link'] def accuracy(self, X=None, y=None, mu=None): """ computes the accuracy of the LogisticGAM Parameters ---------- note: X or mu must be defined. defaults to mu X : array-like of shape (n_samples, m_features), optional (default=None) containing input data y : array-like of shape (n,) containing target data mu : array-like of shape (n_samples,), optional (default=None expected value of the targets given the model and inputs Returns ------- float in [0, 1] """ if not self._is_fitted: raise AttributeError('GAM has not been fitted. Call fit first.') y = check_y(y, self.link, self.distribution, verbose=self.verbose) if X is not None: X = check_X(X, n_feats=self.statistics_['m_features'], edge_knots=self.edge_knots_, dtypes=self.dtype, features=self.feature, verbose=self.verbose) if mu is None: mu = self.predict_mu(X) check_X_y(mu, y) return ((mu > 0.5).astype(int) == y).mean() def predict(self, X): """ preduct binary targets given model and input X Parameters --------- X : array-like of shape (n_samples, m_features), optional (default=None) containing the input dataset Returns ------- y : np.array of shape (n_samples,) containing binary targets under the model """ return self.predict_mu(X) > 0.5 def predict_proba(self, X): """ preduct targets given model and input X Parameters --------- X : array-like of shape (n_samples, m_features), optional (default=None containing the input dataset Returns ------- y : np.array of shape (n_samples,) containing expected values under the model """ return self.predict_mu(X) class PoissonGAM(GAM): """Poisson GAM This is a GAM with a Poisson error distribution, and a log link. Parameters ---------- terms : expression specifying terms to model, optional. By default a univariate spline term will be allocated for each feature. For example: >>> GAM(s(0) + l(1) + f(2) + te(3, 4)) will fit a spline term on feature 0, a linear term on feature 1, a factor term on feature 2, and a tensor term on features 3 and 4. callbacks : list of str or list of CallBack objects, optional Names of callback objects to call during the optimization loop. fit_intercept : bool, optional Specifies if a constant (a.k.a. bias or intercept) should be added to the decision function. Note: the intercept receives no smoothing penalty. max_iter : int, optional Maximum number of iterations allowed for the solver to converge. tol : float, optional Tolerance for stopping criteria. verbose : bool, optional whether to show pyGAM warnings. Attributes ---------- coef_ : array, shape (n_classes, m_features) Coefficient of the features in the decision function. If fit_intercept is True, then self.coef_[0] will contain the bias. statistics_ : dict Dictionary containing model statistics like GCV/UBRE scores, AIC/c, parameter covariances, estimated degrees of freedom, etc. logs_ : dict Dictionary containing the outputs of any callbacks at each optimization loop. The logs are structured as ``{callback: [...]}`` References ---------- Simon N. Wood, 2006 Generalized Additive Models: an introduction with R Hastie, Tibshirani, Friedman The Elements of Statistical Learning http://statweb.stanford.edu/~tibs/ElemStatLearn/printings/ESLII_print10.pdf Paul Eilers & Brian Marx, 2015 International Biometric Society: A Crash Course on P-splines http://www.ibschannel2015.nl/project/userfiles/Crash_course_handout.pdf """ def __init__(self, terms='auto', max_iter=100, tol=1e-4, callbacks=['deviance', 'diffs'], fit_intercept=True, verbose=False, **kwargs): # call super super(PoissonGAM, self).__init__(terms=terms, distribution='poisson', link='log', max_iter=max_iter, tol=tol, callbacks=callbacks, fit_intercept=fit_intercept, verbose=verbose, **kwargs) # ignore any variables self._exclude += ['distribution', 'link'] def _loglikelihood(self, y, mu, weights=None, rescale_y=True): """ compute the log-likelihood of the dataset using the current model Parameters --------- y : array-like of shape (n,) containing target values mu : array-like of shape (n_samples,) expected value of the targets given the model and inputs weights : array-like of shape (n,) containing sample weights rescale_y : boolean, defaul: True whether to scale the targets back up. useful when fitting with an exposure, in which case the count observations were scaled into rates. this rescales rates into counts. Returns ------- log-likelihood : np.array of shape (n,) containing log-likelihood scores """ if rescale_y: y = np.round(y * weights).astype('int') return self.distribution.log_pdf(y=y, mu=mu, weights=weights).sum() def loglikelihood(self, X, y, exposure=None, weights=None): """ compute the log-likelihood of the dataset using the current model Parameters --------- X : array-like of shape (n_samples, m_features) containing the input dataset y : array-like of shape (n,) containing target values exposure : array-like shape (n_samples,) or None, default: None containing exposures if None, defaults to array of ones weights : array-like of shape (n,) containing sample weights Returns ------- log-likelihood : np.array of shape (n,) containing log-likelihood scores """ y = check_y(y, self.link, self.distribution, verbose=self.verbose) mu = self.predict_mu(X) if weights is not None: weights = np.array(weights).astype('f').ravel() weights = check_array(weights, name='sample weights', ndim=1, verbose=self.verbose) check_lengths(y, weights) else: weights = np.ones_like(y).astype('float64') y, weights = self._exposure_to_weights(y, exposure, weights) return self._loglikelihood(y, mu, weights=weights, rescale_y=True) def _exposure_to_weights(self, y, exposure=None, weights=None): """simple tool to create a common API Parameters ---------- y : array-like, shape (n_samples,) Target values (integers in classification, real numbers in regression) For classification, labels must correspond to classes. exposure : array-like shape (n_samples,) or None, default: None containing exposures if None, defaults to array of ones weights : array-like shape (n_samples,) or None, default: None containing sample weights if None, defaults to array of ones Returns ------- y : y normalized by exposure weights : array-like shape (n_samples,) """ y = y.ravel() if exposure is not None: exposure = np.array(exposure).astype('f').ravel() exposure = check_array(exposure, name='sample exposure', ndim=1, verbose=self.verbose) else: exposure = np.ones_like(y.ravel()).astype('float64') # check data exposure = exposure.ravel() check_lengths(y, exposure) # normalize response y = y / exposure if weights is not None: weights = np.array(weights).astype('f').ravel() weights = check_array(weights, name='sample weights', ndim=1, verbose=self.verbose) else: weights = np.ones_like(y).astype('float64') check_lengths(weights, exposure) # set exposure as the weight # we do this because we have divided our response # so if we make an error of 1 now, we need it to count more heavily. weights = weights * exposure return y, weights def fit(self, X, y, exposure=None, weights=None): """Fit the generalized additive model. Parameters ---------- X : array-like, shape (n_samples, m_features) Training vectors, where n_samples is the number of samples and m_features is the number of features. y : array-like, shape (n_samples,) Target values (integers in classification, real numbers in regression) For classification, labels must correspond to classes. exposure : array-like shape (n_samples,) or None, default: None containing exposures if None, defaults to array of ones weights : array-like shape (n_samples,) or None, default: None containing sample weights if None, defaults to array of ones Returns ------- self : object Returns fitted GAM object """ y, weights = self._exposure_to_weights(y, exposure, weights) return super(PoissonGAM, self).fit(X, y, weights) def predict(self, X, exposure=None): """ preduct expected value of target given model and input X often this is done via expected value of GAM given input X Parameters --------- X : array-like of shape (n_samples, m_features), default: None containing the input dataset exposure : array-like shape (n_samples,) or None, default: None containing exposures if None, defaults to array of ones Returns ------- y : np.array of shape (n_samples,) containing predicted values under the model """ if not self._is_fitted: raise AttributeError('GAM has not been fitted. Call fit first.') X = check_X(X, n_feats=self.statistics_['m_features'], edge_knots=self.edge_knots_, dtypes=self.dtype, features=self.feature, verbose=self.verbose) if exposure is not None: exposure = np.array(exposure).astype('f') else: exposure = np.ones(X.shape[0]).astype('f') check_lengths(X, exposure) return self.predict_mu(X) * exposure def gridsearch(self, X, y, exposure=None, weights=None, return_scores=False, keep_best=True, objective='auto', **param_grids): """ performs a grid search over a space of parameters for a given objective NOTE: gridsearch method is lazy and will not remove useless combinations from the search space, eg. >>> n_splines=np.arange(5,10), fit_splines=[True, False] will result in 10 loops, of which 5 are equivalent because even though fit_splines==False it is not recommended to search over a grid that alternates between known scales and unknown scales, as the scores of the candidate models will not be comparable. Parameters ---------- X : array input data of shape (n_samples, m_features) y : array label data of shape (n_samples,) exposure : array-like shape (n_samples,) or None, default: None containing exposures if None, defaults to array of ones weights : array-like shape (n_samples,) or None, default: None containing sample weights if None, defaults to array of ones return_scores : boolean, default False whether to return the hyperpamaters and score for each element in the grid keep_best : boolean whether to keep the best GAM as self. default: True objective : string, default: 'auto' metric to optimize. must be in ['AIC', 'AICc', 'GCV', 'UBRE', 'auto'] if 'auto', then grid search will optimize GCV for models with unknown scale and UBRE for models with known scale. **kwargs : dict, default {'lam': np.logspace(-3, 3, 11)} pairs of parameters and iterables of floats, or parameters and iterables of iterables of floats. if iterable of iterables of floats, the outer iterable must have length m_features. the method will make a grid of all the combinations of the parameters and fit a GAM to each combination. Returns ------- if return_values == True: model_scores : dict Contains each fitted model as keys and corresponding objective scores as values else: self, ie possibly the newly fitted model """ y, weights = self._exposure_to_weights(y, exposure, weights) return super(PoissonGAM, self).gridsearch(X, y, weights=weights, return_scores=return_scores, keep_best=keep_best, objective=objective, **param_grids) class GammaGAM(GAM): """Gamma GAM This is a GAM with a Gamma error distribution, and a log link. NB Although canonical link function for the Gamma GLM is the inverse link, this function can create problems for numerical software because it becomes difficult to enforce the requirement that the mean of the Gamma distribution be positive. The log link guarantees this. If you need to use the inverse link function, simply construct a custom GAM: >>> from pygam import GAM >>> gam = GAM(distribution='gamma', link='inverse') Parameters ---------- terms : expression specifying terms to model, optional. By default a univariate spline term will be allocated for each feature. For example: >>> GAM(s(0) + l(1) + f(2) + te(3, 4)) will fit a spline term on feature 0, a linear term on feature 1, a factor term on feature 2, and a tensor term on features 3 and 4. callbacks : list of str or list of CallBack objects, optional Names of callback objects to call during the optimization loop. fit_intercept : bool, optional Specifies if a constant (a.k.a. bias or intercept) should be added to the decision function. Note: the intercept receives no smoothing penalty. max_iter : int, optional Maximum number of iterations allowed for the solver to converge. tol : float, optional Tolerance for stopping criteria. verbose : bool, optional whether to show pyGAM warnings. Attributes ---------- coef_ : array, shape (n_classes, m_features) Coefficient of the features in the decision function. If fit_intercept is True, then self.coef_[0] will contain the bias. statistics_ : dict Dictionary containing model statistics like GCV/UBRE scores, AIC/c, parameter covariances, estimated degrees of freedom, etc. logs_ : dict Dictionary containing the outputs of any callbacks at each optimization loop. The logs are structured as ``{callback: [...]}`` References ---------- Simon N. Wood, 2006 Generalized Additive Models: an introduction with R Hastie, Tibshirani, Friedman The Elements of Statistical Learning http://statweb.stanford.edu/~tibs/ElemStatLearn/printings/ESLII_print10.pdf Paul Eilers & Brian Marx, 2015 International Biometric Society: A Crash Course on P-splines http://www.ibschannel2015.nl/project/userfiles/Crash_course_handout.pdf """ def __init__(self, terms='auto', max_iter=100, tol=1e-4, scale=None, callbacks=['deviance', 'diffs'], fit_intercept=True, verbose=False, **kwargs): self.scale = scale super(GammaGAM, self).__init__(terms=terms, distribution=GammaDist(scale=self.scale), link='log', max_iter=max_iter, tol=tol, callbacks=callbacks, fit_intercept=fit_intercept, verbose=verbose, **kwargs) self._exclude += ['distribution', 'link'] def _validate_params(self): """ method to sanitize model parameters Parameters --------- None Returns ------- None """ self.distribution = GammaDist(scale=self.scale) super(GammaGAM, self)._validate_params() class InvGaussGAM(GAM): """Inverse Gaussian GAM This is a GAM with a Inverse Gaussian error distribution, and a log link. NB Although canonical link function for the Inverse Gaussian GLM is the inverse squared link, this function can create problems for numerical software because it becomes difficult to enforce the requirement that the mean of the Inverse Gaussian distribution be positive. The log link guarantees this. If you need to use the inverse squared link function, simply construct a custom GAM: >>> from pygam import GAM >>> gam = GAM(distribution='inv_gauss', link='inv_squared') Parameters ---------- terms : expression specifying terms to model, optional. By default a univariate spline term will be allocated for each feature. For example: >>> GAM(s(0) + l(1) + f(2) + te(3, 4)) will fit a spline term on feature 0, a linear term on feature 1, a factor term on feature 2, and a tensor term on features 3 and 4. callbacks : list of str or list of CallBack objects, optional Names of callback objects to call during the optimization loop. fit_intercept : bool, optional Specifies if a constant (a.k.a. bias or intercept) should be added to the decision function. Note: the intercept receives no smoothing penalty. max_iter : int, optional Maximum number of iterations allowed for the solver to converge. tol : float, optional Tolerance for stopping criteria. verbose : bool, optional whether to show pyGAM warnings. Attributes ---------- coef_ : array, shape (n_classes, m_features) Coefficient of the features in the decision function. If fit_intercept is True, then self.coef_[0] will contain the bias. statistics_ : dict Dictionary containing model statistics like GCV/UBRE scores, AIC/c, parameter covariances, estimated degrees of freedom, etc. logs_ : dict Dictionary containing the outputs of any callbacks at each optimization loop. The logs are structured as ``{callback: [...]}`` References ---------- Simon N. Wood, 2006 Generalized Additive Models: an introduction with R Hastie, Tibshirani, Friedman The Elements of Statistical Learning http://statweb.stanford.edu/~tibs/ElemStatLearn/printings/ESLII_print10.pdf Paul Eilers & Brian Marx, 2015 International Biometric Society: A Crash Course on P-splines http://www.ibschannel2015.nl/project/userfiles/Crash_course_handout.pdf """ def __init__(self, terms='auto', max_iter=100, tol=1e-4, scale=None, callbacks=['deviance', 'diffs'], fit_intercept=True, verbose=False, **kwargs): self.scale = scale super(InvGaussGAM, self).__init__(terms=terms, distribution=InvGaussDist(scale=self.scale), link='log', max_iter=max_iter, tol=tol, callbacks=callbacks, fit_intercept=fit_intercept, verbose=verbose, **kwargs) self._exclude += ['distribution', 'link'] def _validate_params(self): """ method to sanitize model parameters Parameters --------- None Returns ------- None """ self.distribution = InvGaussDist(scale=self.scale) super(InvGaussGAM, self)._validate_params() class ExpectileGAM(GAM): """Expectile GAM This is a GAM with a Normal distribution and an Identity Link, but minimizing the Least Asymmetrically Weighted Squares Parameters ---------- terms : expression specifying terms to model, optional. By default a univariate spline term will be allocated for each feature. For example: >>> GAM(s(0) + l(1) + f(2) + te(3, 4)) will fit a spline term on feature 0, a linear term on feature 1, a factor term on feature 2, and a tensor term on features 3 and 4. callbacks : list of str or list of CallBack objects, optional Names of callback objects to call during the optimization loop. fit_intercept : bool, optional Specifies if a constant (a.k.a. bias or intercept) should be added to the decision function. Note: the intercept receives no smoothing penalty. max_iter : int, optional Maximum number of iterations allowed for the solver to converge. tol : float, optional Tolerance for stopping criteria. verbose : bool, optional whether to show pyGAM warnings. Attributes ---------- coef_ : array, shape (n_classes, m_features) Coefficient of the features in the decision function. If fit_intercept is True, then self.coef_[0] will contain the bias. statistics_ : dict Dictionary containing model statistics like GCV/UBRE scores, AIC/c, parameter covariances, estimated degrees of freedom, etc. logs_ : dict Dictionary containing the outputs of any callbacks at each optimization loop. The logs are structured as ``{callback: [...]}`` References ---------- Simon N. Wood, 2006 Generalized Additive Models: an introduction with R Hastie, Tibshirani, Friedman The Elements of Statistical Learning http://statweb.stanford.edu/~tibs/ElemStatLearn/printings/ESLII_print10.pdf Paul Eilers & Brian Marx, 2015 International Biometric Society: A Crash Course on P-splines http://www.ibschannel2015.nl/project/userfiles/Crash_course_handout.pdf """ def __init__(self, terms='auto', max_iter=100, tol=1e-4, scale=None, callbacks=['deviance', 'diffs'], fit_intercept=True, expectile=0.5, verbose=False, **kwargs): self.scale = scale self.expectile = expectile super(ExpectileGAM, self).__init__(terms=terms, distribution=NormalDist(scale=self.scale), link='identity', max_iter=max_iter, tol=tol, callbacks=callbacks, fit_intercept=fit_intercept, verbose=verbose, **kwargs) self._exclude += ['distribution', 'link'] def _validate_params(self): """ method to sanitize model parameters Parameters --------- None Returns ------- None """ if self.expectile >= 1 or self.expectile <= 0: raise ValueError('expectile must be in (0,1), but found {}'.format(self.expectile)) self.distribution = NormalDist(scale=self.scale) super(ExpectileGAM, self)._validate_params() def _W(self, mu, weights, y=None): """ compute the PIRLS weights for model predictions. TODO lets verify the formula for this. if we use the square root of the mu with the stable opt, we get the same results as when we use non-sqrt mu with naive opt. this makes me think that they are equivalent. also, using non-sqrt mu with stable opt gives very small edofs for even lam=0.001 and the parameter variance is huge. this seems strange to me. computed [V * d(link)/d(mu)] ^(-1/2) by hand and the math checks out as hoped. ive since moved the square to the naive pirls method to make the code modular. Parameters --------- mu : array-like of shape (n_samples,) expected value of the targets given the model and inputs weights : array-like of shape (n_samples,) containing sample weights y = array-like of shape (n_samples,) or None, default None useful for computing the asymmetric weight. Returns ------- weights : scipy.sparse array of shape (n_samples, n_samples) """ # asymmetric weight asym = (y > mu) * self.expectile + (y <= mu) * (1 - self.expectile) return sp.sparse.diags((self.link.gradient(mu, self.distribution)**2 * self.distribution.V(mu=mu) * weights ** -1)**-0.5 * asym**0.5) def _get_quantile_ratio(self, X, y): """find the expirical quantile of the model Parameters ---------- X : array-like, shape (n_samples, m_features) Training vectors, where n_samples is the number of samples and m_features is the number of features. y : array-like, shape (n_samples,) Target values (integers in classification, real numbers in regression) For classification, labels must correspond to classes. Returns ------- ratio : float on [0, 1] """ y_pred = self.predict(X) return (y_pred > y).mean() def fit_quantile(self, X, y, quantile, max_iter=20, tol=0.01, weights=None): """fit ExpectileGAM to a desired quantile via binary search Parameters ---------- X : array-like, shape (n_samples, m_features) Training vectors, where n_samples is the number of samples and m_features is the number of features. y : array-like, shape (n_samples,) Target values (integers in classification, real numbers in regression) For classification, labels must correspond to classes. quantile : float on (0, 1) desired quantile to fit. max_iter : int, default: 20 maximum number of binary search iterations to perform tol : float > 0, default: 0.01 maximum distance between desired quantile and fitted quantile weights : array-like shape (n_samples,) or None, default: None containing sample weights if None, defaults to array of ones Returns ------- self : fitted GAM object """ def _within_tol(a, b, tol): return np.abs(a - b) <= tol # validate arguments if quantile <= 0 or quantile >= 1: raise ValueError('quantile must be on (0, 1), but found {}'.format(quantile)) if tol <= 0: raise ValueError('tol must be float > 0 {}'.format(tol)) if max_iter <= 0: raise ValueError('max_iter must be int > 0 {}'.format(max_iter)) # perform a first fit if necessary if not self._is_fitted: self.fit(X, y, weights=weights) # do binary search max_ = 1.0 min_ = 0.0 n_iter = 0 while n_iter < max_iter: ratio = self._get_quantile_ratio(X, y) if _within_tol(ratio, quantile, tol): break if ratio < quantile: min_ = self.expectile else: max_ = self.expectile expectile = (max_ + min_) / 2. self.set_params(expectile=expectile) self.fit(X, y, weights=weights) n_iter += 1 # print diagnostics if not _within_tol(ratio, quantile, tol) and self.verbose: warnings.warn('maximum iterations reached') return self PK _Mn_Cpygam/terms.py""" Link functions """ from __future__ import division, absolute_import from abc import ABCMeta from abc import abstractmethod, abstractproperty from collections import defaultdict import warnings from copy import deepcopy import numpy as np import scipy as sp from pygam.core import Core, nice_repr from pygam.utils import isiterable, check_param, flatten, gen_edge_knots, b_spline_basis, tensor_product from pygam.penalties import PENALTIES, CONSTRAINTS class Term(Core): __metaclass__ = ABCMeta def __init__(self, feature, lam=0.6, dtype='numerical', fit_linear=False, fit_splines=True, penalties='auto', constraints=None, verbose=False): """creates an instance of a Term Parameters ---------- feature : int Index of the feature to use for the feature function. lam : float or iterable of floats Strength of smoothing penalty. Must be a positive float. Larger values enforce stronger smoothing. If single value is passed, it will be repeated for every penalty. If iterable is passed, the length of `lam` must be equal to the length of `penalties` penalties : {'auto', 'derivative', 'l2', None} or callable or iterable Type of smoothing penalty to apply to the term. If an iterable is used, multiple penalties are applied to the term. The length of the iterable must match the length of `lam`. If 'auto', then 2nd derivative smoothing for 'numerical' dtypes, and L2/ridge smoothing for 'categorical' dtypes. Custom penalties can be passed as a callable. constraints : {None, 'convex', 'concave', 'monotonic_inc', 'monotonic_dec'} or callable or iterable Type of constraint to apply to the term. If an iterable is used, multiple penalties are applied to the term. dtype : {'numerical', 'categorical'} String describing the data-type of the feature. fit_linear : bool whether to fit a linear model of the feature fit_splines : bool whether to fit spliens to the feature Attributes ---------- n_coefs : int Number of coefficients contributed by the term to the model istensor : bool whether the term is a tensor product of sub-terms isintercept : bool whether the term is an intercept hasconstraint : bool whether the term has any constraints info : dict contains dict with the sufficient information to duplicate the term """ self.feature = feature self.lam = lam self.dtype = dtype self.fit_linear = fit_linear self.fit_splines = fit_splines self.penalties = penalties self.constraints = constraints self.verbose = verbose if not(hasattr(self, '_name')): self._name = 'term' super(Term, self).__init__(name=self._name) self._validate_arguments() def __len__(self): return 1 def __eq__(self, other): if isinstance(other, Term): return self.info == other.info return False def __radd__(self, other): return TermList(other, self) def __add__(self, other): return TermList(self, other) def __mul__(self, other): raise NotImplementedError() def __repr__(self): if hasattr(self, '_minimal_name'): name = self._minimal_name else: name = self.__class__.__name__ features = [] if self.feature is None else self.feature features = np.atleast_1d(features).tolist() return nice_repr(name, {}, line_width=self._line_width, line_offset=self._line_offset, decimals=4, args=features) def _validate_arguments(self): """method to sanitize model parameters Parameters --------- None Returns ------- None """ # dtype if self.dtype not in ['numerical', 'categorical']: raise ValueError("dtype must be in ['numerical','categorical'], "\ "but found dtype = {}".format(self.dtype)) # fit_linear XOR fit_splines if self.fit_linear == self.fit_splines: raise ValueError('term must have fit_linear XOR fit_splines, but found: ' 'fit_linear= {}, fit_splines={}'.format(self.fit_linear, self.fit_splines)) # penalties if not isiterable(self.penalties): self.penalties = [self.penalties] for i, p in enumerate(self.penalties): if not (hasattr(p, '__call__') or (p in PENALTIES) or (p is None)): raise ValueError("penalties must be callable or in "\ "{}, but found {} for {}th penalty"\ .format(list(PENALTIES.keys()), p, i)) # check lams and distribute to penalites if not isiterable(self.lam): self.lam = [self.lam] for lam in self.lam: check_param(lam, param_name='lam', dtype='float', constraint='>= 0') if len(self.lam) == 1: self.lam = self.lam * len(self.penalties) if len(self.lam) != len(self.penalties): raise ValueError('expected 1 lam per penalty, but found '\ 'lam = {}, penalties = {}'.format(self.lam, self.penalties)) # constraints if not isiterable(self.constraints): self.constraints = [self.constraints] for i, c in enumerate(self.constraints): if not (hasattr(c, '__call__') or (c in CONSTRAINTS) or (c is None)): raise ValueError("constraints must be callable or in "\ "{}, but found {} for {}th constraint"\ .format(list(CONSTRAINTS.keys()), c, i)) return self @property def istensor(self): return isinstance(self, TensorTerm) @property def isintercept(self): return isinstance(self, Intercept) @property def info(self): """get information about this term Parameters ---------- Returns ------- dict containing information to duplicate this term """ info = self.get_params() info.update({'term_type': self._name}) return info @classmethod def build_from_info(cls, info): """build a Term instance from a dict Parameters ---------- cls : class info : dict contains all information needed to build the term Return ------ Term instance """ info = deepcopy(info) if 'term_type' in info: cls_ = TERMS[info.pop('term_type')] if issubclass(cls_, MetaTermMixin): return cls_.build_from_info(info) else: cls_ = cls return cls_(**info) @property def hasconstraint(self): """bool, whether the term has any constraints """ return np.not_equal(np.atleast_1d(self.constraints), None).any() @property @abstractproperty def n_coefs(self): """Number of coefficients contributed by the term to the model """ pass @abstractmethod def compile(self, X, verbose=False): """method to validate and prepare data-dependent parameters Parameters --------- X : array-like Input dataset verbose : bool whether to show warnings Returns ------- None """ return self @abstractmethod def build_columns(self, X, verbose=False): """construct the model matrix columns for the term Parameters ---------- X : array-like Input dataset with n rows verbose : bool whether to show warnings Returns ------- scipy sparse array with n rows """ pass def build_penalties(self, verbose=False): """ builds the GAM block-diagonal penalty matrix in quadratic form out of penalty matrices specified for each feature. each feature penalty matrix is multiplied by a lambda for that feature. so for m features: P = block_diag[lam0 * P0, lam1 * P1, lam2 * P2, ... , lamm * Pm] Parameters --------- None Returns ------- P : sparse CSC matrix containing the model penalties in quadratic form """ if self.isintercept: return np.array([[0.]]) Ps = [] for penalty, lam in zip(self.penalties, self.lam): if penalty == 'auto': if self.dtype == 'numerical': if self._name == 'spline_term': if self.basis in ['cp']: penalty = 'periodic' else: penalty = 'derivative' else: penalty = 'l2' if self.dtype == 'categorical': penalty = 'l2' if penalty is None: penalty = 'none' if penalty in PENALTIES: penalty = PENALTIES[penalty] P = penalty(self.n_coefs, coef=None) # penalties dont need coef Ps.append(np.multiply(P, lam)) return np.sum(Ps) def build_constraints(self, coef, constraint_lam, constraint_l2): """ builds the GAM block-diagonal constraint matrix in quadratic form out of constraint matrices specified for each feature. behaves like a penalty, but with a very large lambda value, ie 1e6. Parameters --------- coefs : array-like containing the coefficients of a term constraint_lam : float, penalty to impose on the constraint. typically this is a very large number. constraint_l2 : float, loading to improve the numerical conditioning of the constraint matrix. typically this is a very small number. Returns ------- C : sparse CSC matrix containing the model constraints in quadratic form """ if self.isintercept: return np.array([[0.]]) Cs = [] for constraint in self.constraints: if constraint is None: constraint = 'none' if constraint in CONSTRAINTS: constraint = CONSTRAINTS[constraint] C = constraint(self.n_coefs, coef) * constraint_lam Cs.append(C) Cs = np.sum(Cs) # improve condition if Cs.nnz > 0: Cs += sp.sparse.diags(constraint_l2 * np.ones(Cs.shape[0])) return Cs class Intercept(Term): def __init__(self, verbose=False): """creates an instance of an Intercept term Parameters ---------- Attributes ---------- n_coefs : int Number of coefficients contributed by the term to the model istensor : bool whether the term is a tensor product of sub-terms isintercept : bool whether the term is an intercept hasconstraint : bool whether the term has any constraints info : dict contains dict with the sufficient information to duplicate the term """ self._name = 'intercept_term' self._minimal_name = 'intercept' super(Intercept, self).__init__(feature=None, fit_linear=False, fit_splines=False, lam=None, penalties=None, constraints=None, verbose=verbose) self._exclude += ['fit_splines', 'fit_linear', 'lam', 'penalties', 'constraints', 'feature', 'dtype'] self._args = [] def __repr__(self): return self._minimal_name def _validate_arguments(self): """method to sanitize model parameters Parameters --------- None Returns ------- None """ return self @property def n_coefs(self): """Number of coefficients contributed by the term to the model """ return 1 def compile(self, X, verbose=False): """method to validate and prepare data-dependent parameters Parameters --------- X : array-like Input dataset verbose : bool whether to show warnings Returns ------- None """ return self def build_columns(self, X, verbose=False): """construct the model matrix columns for the term Parameters ---------- X : array-like Input dataset with n rows verbose : bool whether to show warnings Returns ------- scipy sparse array with n rows """ return sp.sparse.csc_matrix(np.ones((len(X), 1))) class LinearTerm(Term): def __init__(self, feature, lam=0.6, penalties='auto', verbose=False): """creates an instance of a LinearTerm Parameters ---------- feature : int Index of the feature to use for the feature function. lam : float or iterable of floats Strength of smoothing penalty. Must be a positive float. Larger values enforce stronger smoothing. If single value is passed, it will be repeated for every penalty. If iterable is passed, the length of `lam` must be equal to the length of `penalties` penalties : {'auto', 'derivative', 'l2', None} or callable or iterable Type of smoothing penalty to apply to the term. If an iterable is used, multiple penalties are applied to the term. The length of the iterable must match the length of `lam`. If 'auto', then 2nd derivative smoothing for 'numerical' dtypes, and L2/ridge smoothing for 'categorical' dtypes. Custom penalties can be passed as a callable. Attributes ---------- n_coefs : int Number of coefficients contributed by the term to the model istensor : bool whether the term is a tensor product of sub-terms isintercept : bool whether the term is an intercept hasconstraint : bool whether the term has any constraints info : dict contains dict with the sufficient information to duplicate the term """ self._name = 'linear_term' self._minimal_name = 'l' super(LinearTerm, self).__init__(feature=feature, lam=lam, penalties=penalties, constraints=None, dtype='numerical', fit_linear=True, fit_splines=False, verbose=verbose) self._exclude += ['fit_splines', 'fit_linear', 'dtype', 'constraints'] @property def n_coefs(self): """Number of coefficients contributed by the term to the model """ return 1 def compile(self, X, verbose=False): """method to validate and prepare data-dependent parameters Parameters --------- X : array-like Input dataset verbose : bool whether to show warnings Returns ------- None """ if self.feature >= X.shape[1]: raise ValueError('term requires feature {}, '\ 'but X has only {} dimensions'\ .format(self.feature, X.shape[1])) self.edge_knots_ = gen_edge_knots(X[:, self.feature], self.dtype, verbose=verbose) return self def build_columns(self, X, verbose=False): """construct the model matrix columns for the term Parameters ---------- X : array-like Input dataset with n rows verbose : bool whether to show warnings Returns ------- scipy sparse array with n rows """ return sp.sparse.csc_matrix(X[:, self.feature][:, np.newaxis]) class SplineTerm(Term): _bases = ['ps', 'cp'] def __init__(self, feature, n_splines=20, spline_order=3, lam=0.6, penalties='auto', constraints=None, dtype='numerical', basis='ps', by=None, edge_knots=None, verbose=False): """creates an instance of a SplineTerm Parameters ---------- feature : int Index of the feature to use for the feature function. n_splines : int Number of splines to use for the feature function. Must be non-negative. spline_order : int Order of spline to use for the feature function. Must be non-negative. lam : float or iterable of floats Strength of smoothing penalty. Must be a positive float. Larger values enforce stronger smoothing. If single value is passed, it will be repeated for every penalty. If iterable is passed, the length of `lam` must be equal to the length of `penalties` penalties : {'auto', 'derivative', 'l2', None} or callable or iterable Type of smoothing penalty to apply to the term. If an iterable is used, multiple penalties are applied to the term. The length of the iterable must match the length of `lam`. If 'auto', then 2nd derivative smoothing for 'numerical' dtypes, and L2/ridge smoothing for 'categorical' dtypes. Custom penalties can be passed as a callable. constraints : {None, 'convex', 'concave', 'monotonic_inc', 'monotonic_dec'} or callable or iterable Type of constraint to apply to the term. If an iterable is used, multiple penalties are applied to the term. dtype : {'numerical', 'categorical'} String describing the data-type of the feature. basis : {'ps', 'cp'} Type of basis function to use in the term. 'ps' : p-spline basis 'cp' : cyclic p-spline basis, useful for building periodic functions. by default, the maximum and minimum of the feature values are used to determine the function's period. to specify a custom period use argument `edge_knots` edge_knots : optional, array-like of floats of length 2 these values specify minimum and maximum domain of the spline function. in the case that `spline_basis="cp"`, `edge_knots` determines the period of the cyclic function. when `edge_knots=None` these values are inferred from the data. default: None by : int, optional Feature to use as a by-variable in the term. For example, if `feature` = 2 `by` = 0, then the term will produce: x0 * f(x2) Attributes ---------- n_coefs : int Number of coefficients contributed by the term to the model istensor : bool whether the term is a tensor product of sub-terms isintercept : bool whether the term is an intercept hasconstraint : bool whether the term has any constraints info : dict contains dict with the sufficient information to duplicate the term """ self.basis = basis self.n_splines = n_splines self.spline_order = spline_order self.by = by self._name = 'spline_term' self._minimal_name = 's' if edge_knots is not None: self.edge_knots_ = edge_knots super(SplineTerm, self).__init__(feature=feature, lam=lam, penalties=penalties, constraints=constraints, fit_linear=False, fit_splines=True, dtype=dtype, verbose=verbose) self._exclude += ['fit_linear', 'fit_splines'] def _validate_arguments(self): """method to sanitize model parameters Parameters --------- None Returns ------- None """ super(SplineTerm, self)._validate_arguments() if self.basis not in self._bases: raise ValueError("basis must be one of {}, "\ "but found: {}".format(self._bases, self.basis)) # n_splines self.n_splines = check_param(self.n_splines, param_name='n_splines', dtype='int', constraint='>= 0') # spline_order self.spline_order = check_param(self.spline_order, param_name='spline_order', dtype='int', constraint='>= 0') # n_splines + spline_order if not self.n_splines > self.spline_order: raise ValueError('n_splines must be > spline_order. '\ 'found: n_splines = {} and spline_order = {}'\ .format(self.n_splines, self.spline_order)) # by if self.by is not None: self.by = check_param(self.by, param_name='by', dtype='int', constraint='>= 0') return self @property def n_coefs(self): """Number of coefficients contributed by the term to the model """ return self.n_splines def compile(self, X, verbose=False): """method to validate and prepare data-dependent parameters Parameters --------- X : array-like Input dataset verbose : bool whether to show warnings Returns ------- None """ if self.feature >= X.shape[1]: raise ValueError('term requires feature {}, '\ 'but X has only {} dimensions'\ .format(self.feature, X.shape[1])) if self.by is not None and self.by >= X.shape[1]: raise ValueError('by variable requires feature {}, '\ 'but X has only {} dimensions'\ .format(self.by, X.shape[1])) if not hasattr(self, 'edge_knots_'): self.edge_knots_ = gen_edge_knots(X[:, self.feature], self.dtype, verbose=verbose) return self def build_columns(self, X, verbose=False): """construct the model matrix columns for the term Parameters ---------- X : array-like Input dataset with n rows verbose : bool whether to show warnings Returns ------- scipy sparse array with n rows """ X[:, self.feature][:, np.newaxis] splines = b_spline_basis(X[:, self.feature], edge_knots=self.edge_knots_, spline_order=self.spline_order, n_splines=self.n_splines, sparse=True, periodic=self.basis in ['cp'], verbose=verbose) if self.by is not None: splines = splines.multiply(X[:, self.by][:, np.newaxis]) return splines class FactorTerm(SplineTerm): _encodings = ['one-hot', 'dummy'] def __init__(self, feature, lam=0.6, penalties='auto', coding='one-hot', verbose=False): """creates an instance of a FactorTerm Parameters ---------- feature : int Index of the feature to use for the feature function. lam : float or iterable of floats Strength of smoothing penalty. Must be a positive float. Larger values enforce stronger smoothing. If single value is passed, it will be repeated for every penalty. If iterable is passed, the length of `lam` must be equal to the length of `penalties` penalties : {'auto', 'derivative', 'l2', None} or callable or iterable Type of smoothing penalty to apply to the term. If an iterable is used, multiple penalties are applied to the term. The length of the iterable must match the length of `lam`. If 'auto', then 2nd derivative smoothing for 'numerical' dtypes, and L2/ridge smoothing for 'categorical' dtypes. Custom penalties can be passed as a callable. coding : {'one-hot'} type of contrast encoding to use. currently, only 'one-hot' encoding has been developed. this means that we fit one coefficient per category. Attributes ---------- n_coefs : int Number of coefficients contributed by the term to the model istensor : bool whether the term is a tensor product of sub-terms isintercept : bool whether the term is an intercept hasconstraint : bool whether the term has any constraints info : dict contains dict with the sufficient information to duplicate the term """ self.coding = coding super(FactorTerm, self).__init__(feature=feature, lam=lam, dtype='categorical', spline_order=0, penalties=penalties, by=None, constraints=None, verbose=verbose) self._name = 'factor_term' self._minimal_name = 'f' self._exclude += ['dtype', 'spline_order', 'by', 'n_splines', 'basis', 'constraints'] def _validate_arguments(self): """method to sanitize model parameters Parameters --------- None Returns ------- None """ super(FactorTerm, self)._validate_arguments() if self.coding not in self._encodings: raise ValueError("coding must be one of {}, "\ "but found: {}".format(self._encodings, self.coding)) return self def compile(self, X, verbose=False): """method to validate and prepare data-dependent parameters Parameters --------- X : array-like Input dataset verbose : bool whether to show warnings Returns ------- None """ super(FactorTerm, self).compile(X) self.n_splines = len(np.unique(X[:, self.feature])) self.edge_knots_ = gen_edge_knots(X[:, self.feature], self.dtype, verbose=verbose) return self def build_columns(self, X, verbose=False): """construct the model matrix columns for the term Parameters ---------- X : array-like Input dataset with n rows verbose : bool whether to show warnings Returns ------- scipy sparse array with n rows """ columns = super(FactorTerm, self).build_columns(X, verbose=verbose) if self.coding == 'dummy': columns = columns[:, 1:] return columns @property def n_coefs(self): """Number of coefficients contributed by the term to the model """ return self.n_splines - 1 * (self.coding in ['dummy']) class MetaTermMixin(object): _plural = [ 'feature', 'dtype', 'fit_linear', 'fit_splines', 'lam', 'n_splines', 'spline_order', 'constraints', 'penalties', 'basis', 'edge_knots_' ] _term_location = '_terms' def _super_get(self, name): return super(MetaTermMixin, self).__getattribute__(name) def _super_has(self, name): try: self._super_get(name) return True except AttributeError: return False def _has_terms(self): """bool, whether the instance has any sub-terms """ loc = self._super_get('_term_location') return self._super_has(loc) \ and isiterable(self._super_get(loc)) \ and len(self._super_get(loc)) > 0 \ and all([isinstance(term, Term) for term in self._super_get(loc)]) def _get_terms(self): """get the terms in the instance Parameters ---------- None Returns ------- list containing terms """ if self._has_terms(): return getattr(self, self._term_location) def __setattr__(self, name, value): if self._has_terms() and name in self._super_get('_plural'): # get the total number of arguments size = np.atleast_1d(flatten(getattr(self, name))).size # check shapes if isiterable(value): value = flatten(value) if len(value) != size: raise ValueError('Expected {} to have length {}, but found {} = {}'\ .format(name, size, name, value)) else: value = [value] * size # now set each term's sequence of arguments for term in self._get_terms()[::-1]: # skip intercept if term.isintercept: continue # how many values does this term get? n = np.atleast_1d(getattr(term, name)).size # get the next n values and set them on this term vals = [value.pop() for _ in range(n)][::-1] setattr(term, name, vals[0] if n == 1 else vals) term._validate_arguments() return super(MetaTermMixin, self).__setattr__(name, value) def __getattr__(self, name): if self._has_terms() and name in self._super_get('_plural'): # collect value from each term values = [] for term in self._get_terms(): # skip the intercept if term.isintercept: continue values.append(getattr(term, name, None)) return values return self._super_get(name) class TensorTerm(SplineTerm, MetaTermMixin): _N_SPLINES = 10 # default num splines def __init__(self, *args, **kwargs): """creates an instance of a TensorTerm This is useful for creating interactions between features, or other terms. Parameters ---------- *args : marginal Terms to combine into a tensor product feature : list of integers Indices of the features to use for the marginal terms. n_splines : list of integers Number of splines to use for each marginal term. Must be of same length as `feature`. spline_order : list of integers Order of spline to use for the feature function. Must be of same length as `feature`. lam : float or iterable of floats Strength of smoothing penalty. Must be a positive float. Larger values enforce stronger smoothing. If single value is passed, it will be repeated for every penalty. If iterable is passed, the length of `lam` must be equal to the length of `penalties` penalties : {'auto', 'derivative', 'l2', None} or callable or iterable Type of smoothing penalty to apply to the term. If an iterable is used, multiple penalties are applied to the term. The length of the iterable must match the length of `lam`. If 'auto', then 2nd derivative smoothing for 'numerical' dtypes, and L2/ridge smoothing for 'categorical' dtypes. Custom penalties can be passed as a callable. constraints : {None, 'convex', 'concave', 'monotonic_inc', 'monotonic_dec'} or callable or iterable Type of constraint to apply to the term. If an iterable is used, multiple penalties are applied to the term. dtype : list of {'numerical', 'categorical'} String describing the data-type of the feature. Must be of same length as `feature`. basis : list of {'ps'} Type of basis function to use in the term. 'ps' : p-spline basis NotImplemented: 'cp' : cyclic p-spline basis Must be of same length as `feature`. by : int, optional Feature to use as a by-variable in the term. For example, if `feature` = [1, 2] `by` = 0, then the term will produce: x0 * te(x1, x2) Attributes ---------- n_coefs : int Number of coefficients contributed by the term to the model istensor : bool whether the term is a tensor product of sub-terms isintercept : bool whether the term is an intercept hasconstraint : bool whether the term has any constraints info : dict contains dict with the sufficient information to duplicate the term """ self.verbose = kwargs.pop('verbose', False) by = kwargs.pop('by', None) terms = self._parse_terms(args, **kwargs) feature = [term.feature for term in terms] super(TensorTerm, self).__init__(feature, by=by, verbose=self.verbose) self._name = 'tensor_term' self._minimal_name = 'te' self._exclude = [ 'feature', 'dtype', 'fit_linear', 'fit_splines', 'lam', 'n_splines', 'spline_order', 'constraints', 'penalties', 'basis', ] for param in self._exclude: delattr(self, param) self._terms = terms def _parse_terms(self, args, **kwargs): m = len(args) if m < 2: raise ValueError('TensorTerm requires at least 2 marginal terms') for k, v in kwargs.items(): if isiterable(v): if len(v) != m: raise ValueError('Expected {} to have length {}, but found {} = {}'\ .format(k, m, k, v)) else: kwargs[k] = [v] * m terms = [] for i, arg in enumerate(np.atleast_1d(args)): if isinstance(arg, TensorTerm): raise ValueError('TensorTerm does not accept other TensorTerms. '\ 'Please build a flat TensorTerm instead of a nested one.') if isinstance(arg, Term): if self.verbose and kwargs: warnings.warn('kwargs are skipped when Term instances are passed to TensorTerm constructor') terms.append(arg) continue kwargs_ = {'n_splines': self._N_SPLINES} kwargs_.update({k: v[i] for k, v in kwargs.items()}) terms.append(SplineTerm(arg, **kwargs_)) return terms def __len__(self): return len(self._terms) def __getitem__(self, i): return self._terms[i] def _validate_arguments(self): """method to sanitize model parameters Parameters --------- None Returns ------- None """ if self._has_terms(): [term._validate_arguments() for term in self._terms] else: super(TensorTerm, self)._validate_arguments() return self @property def info(self): """get information about this term Parameters ---------- Returns ------- dict containing information to duplicate this term """ info = super(TensorTerm, self).info info.update({'terms':[term.info for term in self._terms]}) return info @classmethod def build_from_info(cls, info): """build a TensorTerm instance from a dict Parameters ---------- cls : class info : dict contains all information needed to build the term Return ------ TensorTerm instance """ terms = [] for term_info in info['terms']: terms.append(SplineTerm.build_from_info(term_info)) return cls(*terms) @property def hasconstraint(self): """bool, whether the term has any constraints """ constrained = False for term in self._terms: constrained = constrained or term.hasconstraint return constrained @property def n_coefs(self): """Number of coefficients contributed by the term to the model """ return np.prod([term.n_coefs for term in self._terms]) def compile(self, X, verbose=False): """method to validate and prepare data-dependent parameters Parameters --------- X : array-like Input dataset verbose : bool whether to show warnings Returns ------- None """ for term in self._terms: term.compile(X, verbose=False) if self.by is not None and self.by >= X.shape[1]: raise ValueError('by variable requires feature {}, '\ 'but X has only {} dimensions'\ .format(self.by, X.shape[1])) return self def build_columns(self, X, verbose=False): """construct the model matrix columns for the term Parameters ---------- X : array-like Input dataset with n rows verbose : bool whether to show warnings Returns ------- scipy sparse array with n rows """ splines = self._terms[0].build_columns(X, verbose=verbose) for term in self._terms[1:]: marginal_splines = term.build_columns(X, verbose=verbose) splines = tensor_product(splines, marginal_splines) if self.by is not None: splines *= X[:, self.by][:, np.newaxis] return sp.sparse.csc_matrix(splines) def build_penalties(self): """ builds the GAM block-diagonal penalty matrix in quadratic form out of penalty matrices specified for each feature. each feature penalty matrix is multiplied by a lambda for that feature. so for m features: P = block_diag[lam0 * P0, lam1 * P1, lam2 * P2, ... , lamm * Pm] Parameters ---------- None Returns ------- P : sparse CSC matrix containing the model penalties in quadratic form """ P = sp.sparse.csc_matrix(np.zeros((self.n_coefs, self.n_coefs))) for i in range(len(self._terms)): P += self._build_marginal_penalties(i) return sp.sparse.csc_matrix(P) def _build_marginal_penalties(self, i): for j, term in enumerate(self._terms): # make appropriate marginal penalty if j == i: P = term.build_penalties() else: P = sp.sparse.eye(term.n_coefs) # compose with other dimensions if j == 0: P_total = P else: P_total = sp.sparse.kron(P_total, P) return P_total def build_constraints(self, coef, constraint_lam, constraint_l2): """ builds the GAM block-diagonal constraint matrix in quadratic form out of constraint matrices specified for each feature. Parameters ---------- coefs : array-like containing the coefficients of a term constraint_lam : float, penalty to impose on the constraint. typically this is a very large number. constraint_l2 : float, loading to improve the numerical conditioning of the constraint matrix. typically this is a very small number. Returns ------- C : sparse CSC matrix containing the model constraints in quadratic form """ C = sp.sparse.csc_matrix(np.zeros((self.n_coefs, self.n_coefs))) for i in range(len(self._terms)): C += self._build_marginal_constraints(i, coef, constraint_lam, constraint_l2) return sp.sparse.csc_matrix(C) def _build_marginal_constraints(self, i, coef, constraint_lam, constraint_l2): """builds a constraint matrix for a marginal term in the tensor term takes a tensor's coef vector, and slices it into pieces corresponding to term i, then builds a constraint matrix for each piece of the coef vector, and assembles them into a composite constraint matrix Parameters ---------- i : int, index of the marginal term for which to build a constraint matrix coefs : array-like containing the coefficients of the tensor term constraint_lam : float, penalty to impose on the constraint. typically this is a very large number. constraint_l2 : float, loading to improve the numerical conditioning of the constraint matrix. typically this is a very small number. Returns ------- C : sparse CSC matrix containing the model constraints in quadratic form """ composite_C = np.zeros((len(coef), len(coef))) for slice_ in self._iterate_marginal_coef_slices(i): # get the slice of coefficient vector coef_slice = coef[slice_] # build the constraint matrix for that slice slice_C = self._terms[i].build_constraints(coef_slice, constraint_lam, constraint_l2) # now enter it into the composite composite_C[tuple(np.meshgrid(slice_, slice_))] = slice_C.A return sp.sparse.csc_matrix(composite_C) def _iterate_marginal_coef_slices(self, i): """iterator of indices into tensor's coef vector for marginal term i's coefs takes a tensor_term and returns an iterator of indices that chop up the tensor's coef vector into slices belonging to term i Parameters ---------- i : int, index of marginal term Yields ------ np.ndarray of ints """ dims = [term_.n_coefs for term_ in self] # make all linear indices idxs = np.arange(np.prod(dims)) # reshape indices to a Nd matrix idxs = idxs.reshape(dims) # reshape to a 2d matrix, where we can loop over rows idxs = np.moveaxis(idxs, i, 0).reshape(idxs.shape[i], int(idxs.size/idxs.shape[i])) # loop over rows for slice_ in idxs.T: yield slice_ class TermList(Core, MetaTermMixin): _terms = [] def __init__(self, *terms, **kwargs): """creates an instance of a TermList If duplicate terms are supplied, only the first instance will be kept. Parameters ---------- *terms : list of terms to verbose : bool whether to show warnings Attributes ---------- n_coefs : int Total number of coefficients in the model hasconstraint : bool whether the model has any constraints info : dict contains dict with the sufficient information to duplicate the term list """ super(TermList, self).__init__() self.verbose = kwargs.pop('verbose', False) if bool(kwargs): raise ValueError("Unexpected keyword argument {}".format(kwargs.keys())) def deduplicate(term, term_list, uniques_dict): """adds a term to the term_list only if it is new Parameters ---------- term : Term new term in consideration term_list : list contains all unique terms uniques_dict : defaultdict keys are term info, values are bool: True if the term has been seen already Returns ------- term_list : list contains `term` if it was unique """ key = str(sorted(term.info.items())) if not uniques_dict[key]: uniques_dict[key] = True term_list.append(term) else: if self.verbose: warnings.warn('skipping duplicate term: {}'.format(repr(term))) return term_list # process terms uniques = defaultdict(bool) term_list = [] for term in terms: if isinstance(term, Term): term_list = deduplicate(term, term_list, uniques) elif isinstance(term, TermList): for term_ in term._terms: term_list = deduplicate(term_, term_list, uniques) else: raise ValueError('terms must be instances of Term or TermList, '\ 'but found term: {}'.format(term)) self._terms = self._terms + term_list self._exclude = [ 'feature', 'dtype', 'fit_linear', 'fit_splines', 'lam', 'n_splines', 'spline_order', 'constraints', 'penalties', 'basis', ] self.verbose = any([term.verbose for term in self._terms]) or self.verbose def __eq__(self, other): if isinstance(other, TermList): return self.info == other.info return False def __repr__(self): return ' + '.join(repr(term) for term in self) def __len__(self): return len(self._terms) def __getitem__(self, i): return self._terms[i] def __radd__(self, other): return TermList(other, self) def __add__(self, other): return TermList(self, other) def __mul__(self, other): raise NotImplementedError() def _validate_arguments(self): """method to sanitize model parameters Parameters --------- None Returns ------- None """ if self._has_terms(): [term._validate_arguments() for term in self._terms] return self @property def info(self): """get information about the terms in the term list Parameters ---------- Returns ------- dict containing information to duplicate the term list """ info = {'term_type': 'term_list', 'verbose': self.verbose} info.update({'terms':[term.info for term in self._terms]}) return info @classmethod def build_from_info(cls, info): """build a TermList instance from a dict Parameters ---------- cls : class info : dict contains all information needed to build the term Return ------ TermList instance """ info = deepcopy(info) terms = [] for term_info in info['terms']: terms.append(Term.build_from_info(term_info)) return cls(*terms) def compile(self, X, verbose=False): """method to validate and prepare data-dependent parameters Parameters --------- X : array-like Input dataset verbose : bool whether to show warnings Returns ------- None """ for term in self._terms: term.compile(X, verbose=verbose) # now remove duplicate intercepts n_intercepts = 0 for term in self._terms: if term.isintercept: n_intercepts += 1 return self def pop(self, i=None): """remove the ith term from the term list Parameters --------- i : int, optional term to remove from term list by default the last term is popped. Returns ------- term : Term """ if i == None: i = len(self) - 1 if i >= len(self._terms) or i < 0: raise ValueError('requested pop {}th term, but found only {} terms'\ .format(i, len(self._terms))) term = self._terms[i] self._terms = self._terms[:i] + self._terms[i+1:] return term @property def hasconstraint(self): """bool, whether the term has any constraints """ constrained = False for term in self._terms: constrained = constrained or term.hasconstraint return constrained @property def n_coefs(self): """Total number of coefficients contributed by the terms in the model """ return sum([term.n_coefs for term in self._terms]) def get_coef_indices(self, i=-1): """get the indices for the coefficients of a term in the term list Parameters --------- i : int by default `int=-1`, meaning that coefficient indices are returned for all terms in the term list Returns ------- list of integers """ if i == -1: return list(range(self.n_coefs)) if i >= len(self._terms): raise ValueError('requested {}th term, but found only {} terms'\ .format(i, len(self._terms))) start = 0 for term in self._terms[:i]: start += term.n_coefs stop = start + self._terms[i].n_coefs return list(range(start, stop)) def build_columns(self, X, term=-1, verbose=False): """construct the model matrix columns for the term Parameters ---------- X : array-like Input dataset with n rows verbose : bool whether to show warnings Returns ------- scipy sparse array with n rows """ if term == -1: term = range(len(self._terms)) term = list(np.atleast_1d(term)) columns = [] for term_id in term: columns.append(self._terms[term_id].build_columns(X, verbose=verbose)) return sp.sparse.hstack(columns, format='csc') def build_penalties(self): """ builds the GAM block-diagonal penalty matrix in quadratic form out of penalty matrices specified for each feature. each feature penalty matrix is multiplied by a lambda for that feature. so for m features: P = block_diag[lam0 * P0, lam1 * P1, lam2 * P2, ... , lamm * Pm] Parameters ---------- None Returns ------- P : sparse CSC matrix containing the model penalties in quadratic form """ P = [] for term in self._terms: P.append(term.build_penalties()) return sp.sparse.block_diag(P) def build_constraints(self, coefs, constraint_lam, constraint_l2): """ builds the GAM block-diagonal constraint matrix in quadratic form out of constraint matrices specified for each feature. behaves like a penalty, but with a very large lambda value, ie 1e6. Parameters --------- coefs : array-like containing the coefficients of a term constraint_lam : float, penalty to impose on the constraint. typically this is a very large number. constraint_l2 : float, loading to improve the numerical conditioning of the constraint matrix. typically this is a very small number. Returns ------- C : sparse CSC matrix containing the model constraints in quadratic form """ C = [] for i, term in enumerate(self._terms): idxs = self.get_coef_indices(i=i) C.append(term.build_constraints(coefs[idxs], constraint_lam, constraint_l2)) return sp.sparse.block_diag(C) # Minimal representations def l(feature, lam=0.6, penalties='auto', verbose=False): """ See Also -------- LinearTerm : for developer details """ return LinearTerm(feature=feature, lam=lam, penalties=penalties, verbose=verbose) def s(feature, n_splines=20, spline_order=3, lam=0.6, penalties='auto', constraints=None, dtype='numerical', basis='ps', by=None, edge_knots=None, verbose=False): """ See Also -------- SplineTerm : for developer details """ return SplineTerm(feature=feature, n_splines=n_splines, spline_order=spline_order, lam=lam, penalties=penalties, constraints=constraints, dtype=dtype, basis=basis, by=by, edge_knots=edge_knots, verbose=verbose) def f(feature, lam=0.6, penalties='auto', coding='one-hot', verbose=False): """ See Also -------- FactorTerm : for developer details """ return FactorTerm(feature=feature, lam=lam, penalties=penalties, coding=coding, verbose=verbose) def te(*args, **kwargs): """ See Also -------- TensorTerm : for developer details """ return TensorTerm(*args, **kwargs) intercept = Intercept() # copy docs for minimal_, class_ in zip([l, s, f, te], [LinearTerm, SplineTerm, FactorTerm, TensorTerm]): minimal_.__doc__ = class_.__init__.__doc__ + minimal_.__doc__ TERMS = {'term' : Term, 'intercept_term' : Intercept, 'linear_term': LinearTerm, 'spline_term': SplineTerm, 'factor_term': FactorTerm, 'tensor_term': TensorTerm, 'term_list': TermList } PKle_Ma}hccpygam/utils.py""" Pygam utilities """ from __future__ import division from copy import deepcopy import numbers import sys import warnings import scipy as sp from scipy import sparse import numpy as np from numpy.linalg import LinAlgError try: from sksparse.cholmod import cholesky as spcholesky from sksparse.test_cholmod import CholmodNotPositiveDefiniteError SKSPIMPORT = True except ImportError: SKSPIMPORT = False class NotPositiveDefiniteError(ValueError): """Exception class to raise if a matrix is not positive definite """ class OptimizationError(ValueError): """Exception class to raise if PIRLS optimization fails """ def cholesky(A, sparse=True, verbose=True): """ Choose the best possible cholesky factorizor. if possible, import the Scikit-Sparse sparse Cholesky method. Permutes the output L to ensure A = L.H . L otherwise defaults to numpy's non-sparse version Parameters ---------- A : array-like array to decompose sparse : boolean, default: True whether to return a sparse array verbose : bool, default: True whether to print warnings """ if SKSPIMPORT: A = sp.sparse.csc_matrix(A) try: F = spcholesky(A) # permutation matrix P P = sp.sparse.lil_matrix(A.shape) p = F.P() P[np.arange(len(p)), p] = 1 # permute L = F.L() L = P.T.dot(L) except CholmodNotPositiveDefiniteError as e: raise NotPositiveDefiniteError('Matrix is not positive definite') if sparse: return L.T # upper triangular factorization return L.T.A # upper triangular factorization else: msg = 'Could not import Scikit-Sparse or Suite-Sparse.\n'\ 'This will slow down optimization for models with '\ 'monotonicity/convexity penalties and many splines.\n'\ 'See installation instructions for installing '\ 'Scikit-Sparse and Suite-Sparse via Conda.' if verbose: warnings.warn(msg) if sp.sparse.issparse(A): A = A.A try: L = sp.linalg.cholesky(A, lower=False) except LinAlgError as e: raise NotPositiveDefiniteError('Matrix is not positive definite') if sparse: return sp.sparse.csc_matrix(L) return L def make_2d(array, verbose=True): """ tiny tool to expand 1D arrays the way i want Parameters ---------- array : array-like verbose : bool, default: True whether to print warnings Returns ------- np.array of with ndim = 2 """ array = np.asarray(array) if array.ndim < 2: msg = 'Expected 2D input data array, but found {}D. '\ 'Expanding to 2D.'.format(array.ndim) if verbose: warnings.warn(msg) array = np.atleast_1d(array)[:,None] return array def check_array(array, force_2d=False, n_feats=None, ndim=None, min_samples=1, name='Input data', verbose=True): """ tool to perform basic data validation. called by check_X and check_y. ensures that data: - is ndim dimensional - contains float-compatible data-types - has at least min_samples - has n_feats - is finite Parameters ---------- array : array-like force_2d : boolean, default: False whether to force a 2d array. Setting to True forces ndim = 2 n_feats : int, default: None represents number of features that the array should have. not enforced if n_feats is None. ndim : int default: None number of dimensions expected in the array min_samples : int, default: 1 name : str, default: 'Input data' name to use when referring to the array verbose : bool, default: True whether to print warnings Returns ------- array : validated array """ # make array if force_2d: array = make_2d(array, verbose=verbose) ndim = 2 else: array = np.array(array) # cast to float dtype = array.dtype if dtype.kind not in ['i', 'f']: try: array = array.astype('float') except ValueError as e: raise ValueError('{} must be type int or float, '\ 'but found type: {}\n'\ 'Try transforming data with a LabelEncoder first.'\ .format(name, dtype.type)) # check finite if not(np.isfinite(array).all()): raise ValueError('{} must not contain Inf nor NaN'.format(name)) # check ndim if ndim is not None: if array.ndim != ndim: raise ValueError('{} must have {} dimensions. '\ 'found shape {}'.format(name, ndim, array.shape)) # check n_feats if n_feats is not None: m = array.shape[1] if m != n_feats: raise ValueError('{} must have {} features, '\ 'but found {}'.format(name, n_feats, m)) # minimum samples n = array.shape[0] if n < min_samples: raise ValueError('{} should have at least {} samples, '\ 'but found {}'.format(name, min_samples, n)) return array def check_y(y, link, dist, min_samples=1, verbose=True): """ tool to ensure that the targets: - are in the domain of the link function - are numerical - have at least min_samples - is finite Parameters ---------- y : array-like link : Link object dist : Distribution object min_samples : int, default: 1 verbose : bool, default: True whether to print warnings Returns ------- y : array containing validated y-data """ y = np.ravel(y) y = check_array(y, force_2d=False, min_samples=min_samples, ndim=1, name='y data', verbose=verbose) with warnings.catch_warnings(): warnings.simplefilter("ignore") if np.any(np.isnan(link.link(y, dist))): raise ValueError('y data is not in domain of {} link function. ' \ 'Expected domain: {}, but found {}' \ .format(link, get_link_domain(link, dist), [float('%.2f'%np.min(y)), float('%.2f'%np.max(y))])) return y def check_X(X, n_feats=None, min_samples=1, edge_knots=None, dtypes=None, features=None, verbose=True): """ tool to ensure that X: - is 2 dimensional - contains float-compatible data-types - has at least min_samples - has n_feats - has categorical features in the right range - is finite Parameters ---------- X : array-like n_feats : int. default: None represents number of features that X should have. not enforced if n_feats is None. min_samples : int, default: 1 edge_knots : list of arrays, default: None dtypes : list of strings, default: None features : list of ints, which features are considered by the model verbose : bool, default: True whether to print warnings Returns ------- X : array with ndims == 2 containing validated X-data """ # check all features are there if bool(features): features = flatten(features) max_feat = max(flatten(features)) if n_feats is None: n_feats = max_feat n_feats = max(n_feats, max_feat) # basic diagnostics X = check_array(X, force_2d=True, n_feats=n_feats, min_samples=min_samples, name='X data', verbose=verbose) # check our categorical data has no new categories if (edge_knots is not None) and (dtypes is not None) and (features is not None): # get a flattened list of tuples edge_knots = flatten(edge_knots)[::-1] dtypes = flatten(dtypes) assert len(edge_knots) % 2 == 0 # sanity check # form pairs n = len(edge_knots) // 2 edge_knots = [(edge_knots.pop(), edge_knots.pop()) for _ in range(n)] # check each categorical term for i, ek in enumerate(edge_knots): dt = dtypes[i] feature = features[i] x = X[:, feature] if dt == 'categorical': min_ = ek[0] max_ = ek[-1] if (np.unique(x) < min_).any() or \ (np.unique(x) > max_).any(): min_ += .5 max_ -= 0.5 raise ValueError('X data is out of domain for categorical '\ 'feature {}. Expected data on [{}, {}], '\ 'but found data on [{}, {}]'\ .format(i, min_, max_, x.min(), x.max())) return X def check_X_y(X, y): """ tool to ensure input and output data have the same number of samples Parameters ---------- X : array-like y : array-like Returns ------- None """ if len(X) != len(y): raise ValueError('Inconsistent input and output data shapes. '\ 'found X: {} and y: {}'.format(X.shape, y.shape)) def check_lengths(*arrays): """ tool to ensure input and output data have the same number of samples Parameters ---------- *arrays : iterable of arrays to be checked Returns ------- None """ lengths = [len(array) for array in arrays] if len(np.unique(lengths)) > 1: raise ValueError('Inconsistent data lengths: {}'.format(lengths)) def check_param(param, param_name, dtype, constraint=None, iterable=True, max_depth=2): """ checks the dtype of a parameter, and whether it satisfies a numerical contraint Parameters --------- param : object param_name : str, name of the parameter dtype : str, desired dtype of the parameter contraint : str, default: None numerical constraint of the parameter. if None, no constraint is enforced iterable : bool, default: True whether to allow iterable param max_depth : int, default: 2 maximum nesting of the iterable. only used if iterable == True Returns ------- list of validated and converted parameter(s) """ msg = [] msg.append(param_name + " must be "+ dtype) if iterable: msg.append(" or nested iterable of depth " + str(max_depth) + " containing " + dtype + "s") msg.append(", but found " + param_name + " = {}".format(repr(param))) if constraint is not None: msg = (" " + constraint).join(msg) else: msg = ''.join(msg) # check param is numerical try: param_dt = np.array(flatten(param))# + np.zeros_like(flatten(param), dtype='int') # param_dt = np.array(param).astype(dtype) except (ValueError, TypeError): raise TypeError(msg) # check iterable if iterable: if check_iterable_depth(param) > max_depth: raise TypeError(msg) if (not iterable) and isiterable(param): raise TypeError(msg) # check param is correct dtype if not (param_dt == np.array(flatten(param)).astype(float)).all(): raise TypeError(msg) # check constraint if constraint is not None: if not (eval('np.' + repr(param_dt) + constraint)).all(): raise ValueError(msg) return param def get_link_domain(link, dist): """ tool to identify the domain of a given monotonic link function Parameters ---------- link : Link object dist : Distribution object Returns ------- domain : list of length 2, representing the interval of the domain. """ domain = np.array([-np.inf, -1, 0, 1, np.inf]) domain = domain[~np.isnan(link.link(domain, dist))] return [domain[0], domain[-1]] def load_diagonal(cov, load=None): """Return the given square matrix with a small amount added to the diagonal to make it positive semi-definite. """ n, m = cov.shape assert n == m, "matrix must be square, but found shape {}".format((n, m)) if load is None: load = np.sqrt(np.finfo(np.float64).eps) # machine epsilon return cov + np.eye(n) * load def round_to_n_decimal_places(array, n=3): """ tool to keep round a float to n decimal places. n=3 by default Parameters ---------- array : np.array n : int. number of decimal places to keep Returns ------- array : rounded np.array """ # check if in scientific notation if issubclass(array.__class__, float) and '%.e'%array == str(array): return array # do nothing shape = np.shape(array) out = ((np.atleast_1d(array) * 10**n).round().astype('int') / (10.**n)) return out.reshape(shape) # Credit to Hugh Bothwell from http://stackoverflow.com/questions/5084743/how-to-print-pretty-string-output-in-python class TablePrinter(object): "Print a list of dicts as a table" def __init__(self, fmt, sep=' ', ul=None): """ @param fmt: list of tuple(heading, key, width) heading: str, column label key: dictionary key to value to print width: int, column width in chars @param sep: string, separation between columns @param ul: string, character to underline column label, or None for no underlining """ super(TablePrinter,self).__init__() self.fmt = str(sep).join('{lb}{0}:{1}{rb}'.format(key, width, lb='{', rb='}') for heading,key,width in fmt) self.head = {key:heading for heading,key,width in fmt} self.ul = {key:str(ul)*width for heading,key,width in fmt} if ul else None self.width = {key:width for heading,key,width in fmt} def row(self, data): if sys.version_info < (3,): return self.fmt.format(**{ k:str(data.get(k,''))[:w] for k,w in self.width.iteritems() }) else: return self.fmt.format(**{ k:str(data.get(k,''))[:w] for k,w in self.width.items() }) def __call__(self, dataList): _r = self.row res = [_r(data) for data in dataList] res.insert(0, _r(self.head)) if self.ul: res.insert(1, _r(self.ul)) return '\n'.join(res) def space_row(left, right, filler=' ', total_width=-1): """space the data in a row with optional filling Arguments --------- left : str, to be aligned left right : str, to be aligned right filler : str, default ' '. must be of length 1 total_width : int, width of line. if negative number is specified, then that number of spaces is used between the left and right text Returns ------- str """ left = str(left) right = str(right) filler = str(filler)[:1] if total_width < 0: spacing = - total_width else: spacing = total_width - len(left) - len(right) return left + filler * spacing + right def sig_code(p_value): """create a significance code in the style of R's lm Arguments --------- p_value : float on [0, 1] Returns ------- str """ assert 0 <= p_value <= 1, 'p_value must be on [0, 1]' if p_value < 0.001: return '***' if p_value < 0.01: return '**' if p_value < 0.05: return '*' if p_value < 0.1: return '.' return ' ' def gen_edge_knots(data, dtype, verbose=True): """ generate uniform knots from data including the edges of the data for discrete data, assumes k categories in [0, k-1] interval Parameters ---------- data : array-like with one dimension dtype : str in {'categorical', 'numerical'} verbose : bool, default: True whether to print warnings Returns ------- np.array containing ordered knots """ if dtype not in ['categorical', 'numerical']: raise ValueError('unsupported dtype: {}'.format(dtype)) if dtype == 'categorical': return np.r_[np.min(data) - 0.5, np.max(data) + 0.5] else: knots = np.r_[np.min(data), np.max(data)] if knots[0] == knots[1] and verbose: warnings.warn('Data contains constant feature. '\ 'Consider removing and setting fit_intercept=True', stacklevel=2) return knots def b_spline_basis(x, edge_knots, n_splines=20, spline_order=3, sparse=True, periodic=True, verbose=True): """ tool to generate b-spline basis using vectorized De Boor recursion the basis functions extrapolate linearly past the end-knots. Parameters ---------- x : array-like, with ndims == 1. edge_knots : array-like contaning locations of the 2 edge knots. n_splines : int. number of splines to generate. must be >= spline_order+1 default: 20 spline_order : int. order of spline basis to create default: 3 sparse : boolean. whether to return a sparse basis matrix or not. default: True verbose : bool, default: True whether to print warnings Returns ------- basis : sparse csc matrix or array containing b-spline basis functions with shape (len(x), n_splines) """ if np.ravel(x).ndim != 1: raise ValueError('Data must be 1-D, but found {}'\ .format(np.ravel(x).ndim)) if (n_splines < 1) or not isinstance(n_splines, numbers.Integral): raise ValueError('n_splines must be int >= 1') if (spline_order < 0) or not isinstance(spline_order, numbers.Integral): raise ValueError('spline_order must be int >= 1') if n_splines < spline_order + 1: raise ValueError('n_splines must be >= spline_order + 1. '\ 'found: n_splines = {} and spline_order = {}'\ .format(n_splines, spline_order)) if n_splines == 0 and verbose: warnings.warn('Requested 1 spline. This is equivalent to '\ 'fitting an intercept', stacklevel=2) n_splines += spline_order * periodic # rescale edge_knots to [0,1], and generate boundary knots edge_knots = np.sort(deepcopy(edge_knots)) offset = edge_knots[0] scale = edge_knots[-1] - edge_knots[0] if scale == 0: scale = 1 boundary_knots = np.linspace(0, 1, 1 + n_splines - spline_order) diff = np.diff(boundary_knots[:2])[0] # rescale x as well x = (np.ravel(deepcopy(x)) - offset) / scale # wrap periodic values if periodic: x = x % (1 + 1e-9) # append 0 and 1 in order to get derivatives for extrapolation x = np.r_[x, 0., 1.] # determine extrapolation indices x_extrapolte_l = (x < 0) x_extrapolte_r = (x > 1) x_interpolate = ~(x_extrapolte_r + x_extrapolte_l) # formatting x = np.atleast_2d(x).T n = len(x) # augment knots aug = np.arange(1, spline_order + 1) * diff aug_knots = np.r_[-aug[::-1], boundary_knots, 1 + aug] aug_knots[-1] += 1e-9 # want last knot inclusive # prepare Haar Basis bases = (x >= aug_knots[:-1]).astype(np.int) * \ (x < aug_knots[1:]).astype(np.int) bases[-1] = bases[-2][::-1] # force symmetric bases at 0 and 1 # do recursion from Hastie et al. vectorized maxi = len(aug_knots) - 1 for m in range(2, spline_order + 2): maxi -= 1 # left sub-basis num = (x - aug_knots[:maxi]) num *= bases[:, :maxi] denom = aug_knots[m-1 : maxi+m-1] - aug_knots[:maxi] left = num/denom # right sub-basis num = (aug_knots[m : maxi+m] - x) * bases[:, 1:maxi+1] denom = aug_knots[m:maxi+m] - aug_knots[1 : maxi+1] right = num/denom # track previous bases and update prev_bases = bases[-2:] bases = left + right if periodic and spline_order > 0: # make spline domain periodic bases[:, :spline_order] = np.max([bases[:, :spline_order], bases[:, -spline_order:]], axis=0) # remove extra splines used only for ensuring correct domain bases = bases[:, :-spline_order] # extrapolate # since we have repeated end-knots, only the last 2 basis functions are # non-zero at the end-knots, and they have equal and opposite gradient. if (any(x_extrapolte_r) or any(x_extrapolte_l)) and spline_order>0: bases[~x_interpolate] = 0. denom = (aug_knots[spline_order:-1] - aug_knots[: -spline_order - 1]) left = prev_bases[:, :-1] / denom denom = (aug_knots[spline_order+1:] - aug_knots[1: -spline_order]) right = prev_bases[:, 1:] / denom grads = (spline_order) * (left - right) if any(x_extrapolte_l): val = grads[0] * x[x_extrapolte_l] + bases[-2] bases[x_extrapolte_l] = val if any(x_extrapolte_r): val = grads[1] * (x[x_extrapolte_r] - 1) + bases[-1] bases[x_extrapolte_r] = val # get rid of the added values at 0, and 1 bases = bases[:-2] if sparse: return sp.sparse.csc_matrix(bases) return bases def ylogydu(y, u): """ tool to give desired output for the limit as y -> 0, which is 0 Parameters ---------- y : array-like of len(n) u : array-like of len(n) Returns ------- np.array len(n) """ mask = (np.atleast_1d(y)!=0.) out = np.zeros_like(u) out[mask] = y[mask] * np.log(y[mask] / u[mask]) return out def combine(*args): """ tool to perform tree search via recursion useful for developing the grid in a grid search Parameters ---------- args : list of lists Returns ------- list of all the combinations of the elements in the input lists """ if hasattr(args, '__iter__') and (len(args) > 1): subtree = combine(*args[:-1]) tree = [] for leaf in subtree: for node in args[-1]: if hasattr(leaf, '__iter__'): tree.append(leaf + [node]) else: tree.append([leaf] + [node]) return tree else: return [[arg] for arg in args[0]] def isiterable(obj, reject_string=True): """convenience tool to detect if something is iterable. in python3, strings count as iterables to we have the option to exclude them Parameters: ----------- obj : object to analyse reject_string : bool, whether to ignore strings Returns: -------- bool, if the object is itereable. """ iterable = hasattr(obj, '__len__') if reject_string: iterable = iterable and not isinstance(obj, str) return iterable def check_iterable_depth(obj, max_depth=100): """find the maximum depth of nesting of the iterable Parameters ---------- obj : iterable max_depth : int, default: 100 maximum depth beyond which we stop counting Returns ------- int """ def find_iterables(obj): iterables = [] for item in obj: if isiterable(item): iterables += list(item) return iterables depth = 0 while (depth < max_depth) and isiterable(obj) and len(obj) > 0: depth += 1 obj = find_iterables(obj) return depth def flatten(iterable): """convenience tool to flatten any nested iterable example: flatten([[[],[4]],[[[5,[6,7, []]]]]]) >>> [4, 5, 6, 7] flatten('hello') >>> 'hello' Parameters ---------- iterable Returns ------- flattened object """ if isiterable(iterable): flat = [] for item in list(iterable): item = flatten(item) if not isiterable(item): item = [item] flat += item return flat else: return iterable def tensor_product(a, b, reshape=True): """ compute the tensor protuct of two matrices a and b if a is (n, m_a), b is (n, m_b), then the result is (n, m_a * m_b) if reshape = True. or (n, m_a, m_b) otherwise Parameters --------- a : array-like of shape (n, m_a) b : array-like of shape (n, m_b) reshape : bool, default True whether to reshape the result to be 2-dimensional ie (n, m_a * m_b) or return a 3-dimensional tensor ie (n, m_a, m_b) Returns ------- dense np.ndarray of shape (n, m_a * m_b) if reshape = True. or (n, m_a, m_b) otherwise """ assert a.ndim == 2, 'matrix a must be 2-dimensional, but found {} dimensions'.format(a.ndim) assert b.ndim == 2, 'matrix b must be 2-dimensional, but found {} dimensions'.format(b.ndim) na, ma = a.shape nb, mb = b.shape if na != nb: raise ValueError('both arguments must have the same number of samples') if sp.sparse.issparse(a): a = a.A if sp.sparse.issparse(b): b = b.A tensor = a[..., :, None] * b[..., None, :] if reshape: return tensor.reshape(na, ma * mb) return tensor PKTSMg@Epygam/datasets/__init__.py""" GAM datasets """ # -*- coding: utf-8 -*- from pygam.datasets.load_datasets import mcycle from pygam.datasets.load_datasets import coal from pygam.datasets.load_datasets import faithful from pygam.datasets.load_datasets import wage from pygam.datasets.load_datasets import trees from pygam.datasets.load_datasets import default from pygam.datasets.load_datasets import cake from pygam.datasets.load_datasets import hepatitis from pygam.datasets.load_datasets import toy_classification from pygam.datasets.load_datasets import head_circumference from pygam.datasets.load_datasets import chicago from pygam.datasets.load_datasets import toy_interaction __all__ = ['mcycle', 'coal', 'faithful', 'trees', 'wage', 'default', 'cake', 'hepatitis', 'toy_classification', 'head_circumference', 'chicago', 'toy_interaction'] PKIMrapygam/datasets/blood1.csv"","SystolicBP","Smoke","Overwt" "1",133,0,2 "2",115,1,0 "3",140,1,1 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4496,119,-15.54872881,-10.67659828,8.6625685076,-1.6338250840000001,1939.5,44.0 4497,90,-12.73901099,,8.2047527138,1.80642578,1940.5,48.0 4498,103,1.1950549451,,14.659255054,1.5893688197,1941.5,51.0 4499,113,-2.71978022,,2.9766660789999997,-2.242483834,1942.5,50.0 4500,113,-19.6043956,,5.9802287643,-2.732509087,1943.5,51.0 4501,109,-16.79945055,,10.392772252,-2.346558951,1944.5,52.0 4502,104,-4.164285714,-8.35505618,7.7200824048,0.1059524644,1945.5,51.0 4503,106,-4.090659341,,7.4230300719,-1.440052102,1946.5,56.0 4504,94,-1.1840659340000002,,19.473871162000002,1.7171436909,1947.5,58.0 4505,114,18.664835165,,16.989773813,2.9816112835000004,1948.5,64.0 4506,144,42.64010989,,18.383982192,2.4360713074,1949.5,67.0 4507,102,41.576923077,,11.959686162,-1.9601275930000002,1950.5,70.0 4508,89,-9.327586207000001,-5.756115819,-4.089270388,-3.407237348,1951.5,58.0 4509,103,-0.8186813190000001,,-4.077614616,-1.421317752,1952.5,56.0 4510,116,-23.85164835,,-11.14096594,-4.830644293,1953.5,53.0 4511,97,-24.90659341,,-5.60729541,-3.9623172980000003,1954.5,51.0 4512,102,-0.049450549,,8.4018855597,-0.298046009,1955.5,58.0 4513,132,30.934065934,,9.7923408799,1.1623960614,1956.5,67.0 4514,100,13.234804208,3.5361507937,3.8836073713999997,-1.08999581,1957.5,62.0 4515,102,-16.07417582,,6.0339885124,-2.902047609,1958.5,51.0 4516,101,-17.18131868,,3.250472475,-2.752924802,1959.5,53.0 4517,107,16.708791209,27.880701754,-2.68968829,-0.253198641,1960.5,60.0 4518,96,11.747252747000001,,14.508607370999998,-1.9417521340000001,1961.5,69.0 4519,116,-1.2664835159999999,,5.7734961357,-1.6732709380000002,1962.5,69.0 4520,93,-15.62711864,-8.682043492,-1.7087026459999999,-3.762517504,1963.5,61.0 4521,104,-7.241758242,,-2.98229541,4.5339177937,1964.5,61.0 4522,95,18.642857143,,13.400965807999999,-0.674758005,1965.5,64.0 4523,118,32.489010989,16.824561404,22.146280365,-0.8980814770000001,1966.5,66.0 4524,91,-23.55494505,,11.089146517,-3.860234255,1967.5,59.0 4525,88,-13.60164835,,-6.44220344,-2.425627774,1968.5,60.0 4526,114,-17.69138418,-11.53629271,-5.505823948,-3.912072241,1969.5,51.0 4527,114,1.4148351648,,4.0756551791,-2.2697206430000003,1970.5,56.0 4528,95,-12.54120879,,0.1716576877,-1.8321940980000002,1971.5,60.0 4529,96,24.519230769,,1.1403744112,3.2014292119,1972.5,64.0 4530,108,10.508241757999999,,5.1796841469,1.7736796116999998,1973.5,75.0 4531,94,13.645604396,,23.83160748,3.2204794005,1974.5,76.0 4532,109,18.333757062,14.701384181,26.295977945,-0.39900557299999995,1975.5,70.0 4533,102,2.8598901099000003,,4.5421391416,-2.014898386,1976.5,73.0 4534,110,-0.107142857,,-6.289072906,-2.89084059,1977.5,65.0 4535,124,-21.06318681,,-9.410853483,-3.4227519660000003,1978.5,64.0 4536,85,-18.23351648,,-1.400536773,-3.6021625680000002,1979.5,58.0 4537,114,-1.28021978,,8.6392672663,-1.991586729,1980.5,64.0 4538,108,-3.122316384,-0.10665664300000001,6.431478423300001,-3.615892285,1981.5,75.0 4539,107,16.813186812999998,,8.750472475,-2.466291457,1982.5,80.0 4540,98,-1.192307692,,13.274818823,-0.843022759,1983.5,81.0 4541,120,3.7225274725,,14.89270459,3.5527060334,1984.5,80.0 4542,107,15.642857142999999,,2.2956699564,0.3422037503,1985.5,79.0 4543,111,24.563186813,,3.741132696,-0.562592922,1986.5,79.0 4544,94,14.066666667,15.513707291,7.5629470314,-1.7724812069999998,1987.5,78.0 4545,88,6.5796703297,17.412727272999998,17.016129893,-2.033310406,1988.5,75.0 4546,114,-15.38736264,,3.854613698,-3.7701663919999997,1989.5,65.0 4547,99,-22.447802199999998,,2.239358436,-3.150721948,1990.5,66.0 4548,102,-27.32692308,,3.0364459632,-3.306971948,1991.5,58.0 4549,102,-15.296703299999999,,2.000472475,-3.3180830589999997,1992.5,61.0 4550,85,-16.55946328,-11.40625929,3.0577965599,-3.298490115,1993.5,57.0 4551,101,-0.28021978,,3.3347928954,-0.592325732,1994.5,59.0 4552,97,-7.2032967029999995,,13.880813184,-0.485744065,1995.5,68.0 4553,101,1.7527472527,10.669811321000001,30.083805808,-0.8797413079999999,1996.5,67.0 4554,123,29.744505495,,25.373765196,1.0522257303,1997.5,72.0 4555,97,46.736263736000005,,8.1879470314,-1.7810262669999999,1998.5,74.0 4556,111,26.357142857,31.580701754,21.165219759,-1.941236168,1999.5,76.0 4557,89,-6.288461538,,3.4868647333999996,-2.6702639169999998,2000.5,76.0 4558,105,10.695054945,,7.6843712564999995,1.5226190475999999,2001.5,75.0 4559,95,7.6236263736000005,9.569811320800001,10.825655179000002,-1.016612934,2002.5,76.0 4560,106,8.6730769231,,15.887465482,1.0998254217,2003.5,78.0 4561,94,18.703296703,,4.3927045899,-2.577466133,2004.5,77.0 4562,94,-9.423728814,-9.827401838,-0.168689867,0.5087665561,2005.5,66.0 4563,98,-2.244505495,,5.1576083077999995,-1.749800051,2006.5,68.0 4564,114,-4.18956044,,2.5474798506,-2.445987099,2007.5,74.0 4565,98,-2.200549451,,4.5777860069,-1.722202975,2008.5,77.0 4566,111,30.793956044,,5.5148720249,-2.4459522519999997,2009.5,84.0 4567,90,8.7589041096,,5.722600599700001,0.6649609315999999,2010.5,86.0 4568,104,1.0,6.4416666667,10.187947031,1.8121666096,2011.5,87.0 4569,113,-7.2054794520000005,,3.4379470314,4.0196214438,2012.5,79.0 4570,116,-9.18630137,,3.6589545947000004,0.2762976716,2013.5,75.0 4571,89,38.756164384,3.0661016949,15.053726321,2.9273320287,2014.5,76.0 4572,105,-2.221917808,,10.000472475,3.365973532,2015.5,76.0 4573,89,-25.23287671,,-0.5411941920000001,-3.5842287010000002,2016.5,64.0 4574,83,-6.268939393999999,-8.507408405,-2.145386302,0.17539138940000001,2017.5,67.0 4575,99,11.761643836,,0.8419407048,2.9467520410000003,2018.5,68.0 4576,103,39.816438356,,8.0421391416,1.7454020311000003,2019.5,70.0 4577,133,62.868493151,,22.104613698,3.2362835235,2020.5,74.0 4578,93,51.84109589,,26.833805808,0.1114875437,2021.5,78.0 4579,115,76.81369863,,21.576463864,-1.3926169330000002,2022.5,82.0 4580,122,-1.025,1.8952939513999998,1.7260379231999998,-2.681658579,2023.5,75.0 4581,89,-4.147945205,,7.7921391416,0.7607276285,2024.5,77.0 4582,96,2.8794520548,,2.125472475,0.8166637016,2025.5,79.0 4583,115,-4.169863014,5.990163934400001,4.0577965599,-2.055025796,2026.5,76.0 4584,98,3.8027397260000004,,5.4641465172000006,-1.774212549,2027.5,83.0 4585,88,-1.082191781,,4.5643269351999995,1.6618837031,2028.5,82.0 4586,95,1.0909090909,1.1126984127,0.3419407048,-1.450309553,2029.5,83.0 4587,110,-15.09863014,,8.2141465172,-0.0022501929999999997,2030.5,82.0 4588,102,-13.136986300000002,,13.920583592,6.99744248,2031.5,85.0 4589,99,16.78630137,2.9885245902,-1.707860858,2.4925338042,2032.5,80.0 4590,121,-6.235616437999999,,1.6879470313999998,0.9953411181999999,2033.5,79.0 4591,98,1.7780821918,,8.494783655099999,1.9748104675,2034.5,82.0 4592,105,10.456214689,5.691337258200001,4.6138770741,-0.947470562,2035.5,83.0 4593,139,30.75890411,,9.1518772471,-1.3877692259999999,2036.5,90.0 4594,139,-3.24109589,,11.819750025,-0.562629896,2037.5,83.0 4595,116,-24.24383562,,1.492713441,-1.616044101,2038.5,74.0 4596,117,-21.26027397,,-5.278296757,-1.5078265080000002,2039.5,71.0 4597,87,-4.271232877,,-1.528882021,2.7831419402999997,2040.5,71.0 4598,93,1.0166666667,-3.652014652,-1.2357327340000002,0.5383330038,2041.5,76.0 4599,102,-13.30410959,-7.184090909,-2.398170284,-0.9456452120000001,2042.5,73.0 4600,107,13.701369863,,4.1010379232,0.5524290381,2043.5,76.0 4601,108,6.7506849314999995,,-3.541194192,-4.045908634,2044.5,72.0 4602,109,-28.29041096,,0.8059339329999999,-5.803164569,2045.5,66.0 4603,105,-3.2684931510000004,,-1.9838701069999998,-2.077253583,2046.5,66.0 4604,107,-0.358333333,-1.3258426970000001,6.5891465172000006,-0.9384470309999999,2047.5,78.0 4605,104,5.6164383562,,-6.666194192000001,-2.462419634,2048.5,75.0 4606,105,-2.3835616440000003,,-10.10371964,-4.144378141000001,2049.5,70.0 4607,102,-2.252054795,,-2.341011488,-3.637108385,2050.5,72.0 4608,100,-28.27671233,,-2.164681513,-5.107085554,2051.5,64.0 4609,73,-19.32054795,,-5.869186816,0.07297013599999999,2052.5,66.0 4610,95,2.7981638418,3.2315151514999996,4.1752928602,3.0679932842,2053.5,73.0 4611,128,0.8082191781,,3.3635278485000004,-1.062056045,2054.5,75.0 4612,87,3.8328767123,,-17.645386300000002,-0.59636345,2055.5,67.0 4613,81,-18.23561644,-6.1890625,-0.5305733810000001,-2.711973046,2056.5,68.0 4614,90,-16.2,,0.050274038099999994,-2.410236935,2057.5,67.0 4615,99,-5.2,,-5.562052969,-0.8773708170000001,2058.5,65.0 4616,124,-0.9218455740000001,1.7402985075,-1.228719635,-3.3690716789999997,2059.5,67.0 4617,98,6.6246575342,,-2.182987451,-2.887896108,2060.5,72.0 4618,99,-0.476712329,,5.125472475,-3.771601687,2061.5,71.0 4619,89,-11.62465753,12.566666667,9.4796406863,-3.36970941,2062.5,70.0 4620,103,-1.569863014,,1.125472475,-2.77265263,2063.5,72.0 4621,87,27.342465753000003,13.26122449,-0.276447029,-0.248268529,2064.5,74.0 4622,105,26.144067796999998,20.323529412,7.492713441,-1.40494897,2065.5,80.0 4623,104,-20.55068493,,7.112801613099999,-3.621550333,2066.5,69.0 4624,98,-16.61643836,,0.22055572699999998,-1.5403464009999999,2067.5,62.0 4625,109,-1.7123287669999998,,-2.108870107,1.6791966384,2068.5,65.0 4626,85,45.328767123,,14.258607370999998,3.4974920197,2069.5,70.0 4627,100,65.323287671,,17.097600600000003,4.8131476255,2070.5,74.0 4628,115,44.091666667,27.366990291,25.365716541999998,5.5883712575,2071.5,76.0 4629,110,30.287671233,,32.391641584,5.572181055,2072.5,79.0 4630,100,23.238356164000002,,31.599463226999998,8.8451472712,2073.5,77.0 4631,100,-21.89863014,,2.1879470314,-2.0685118,2074.5,66.0 4632,98,-7.917808218999999,,-10.78459474,0.7123659594,2075.5,65.0 4633,100,2.8684931507,,-4.416194192,-0.550930646,2076.5,71.0 4634,90,5.5083333333,-9.792957746,-11.02553994,-1.714230032,2077.5,62.0 4635,97,15.843835616,,-9.48229541,0.3640013083,2078.5,62.0 4636,93,7.8712328767,,-3.562052969,3.4496947266,2079.5,64.0 4637,106,-5.128767123,,0.7558131839,1.6487080213,2080.5,68.0 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7020,60.5,20.81 7021,59.9,20.81 7022,56.6,20.82 7023,58.0,20.83 7024,54.0,20.84 7025,58.5,20.85 7026,58.5,20.86 7027,60.5,20.88 7028,60.1,20.89 7029,58.5,20.89 7030,59.0,20.95 7031,58.0,20.98 7032,59.5,21.01 7033,57.0,21.03 7034,60.0,21.09 7035,58.1,21.09 7036,59.0,21.14 7037,55.5,21.27 7038,57.0,21.47 7039,58.5,21.68 PKIM%9'pygam/datasets/hepatitis_A_bulgaria.csv"age","hepatitis_A_positive","total" 1,3,16 2,3,15 3,3,16 4,4,13 5,7,12 6,4,15 7,3,12 8,4,11 9,7,10 10,8,15 11,2,7 12,3,7 13,2,11 14,0,1 15,5,16 16,13,41 17,1,2 18,3,6 19,15,32 20,22,37 21,15,24 22,7,10 23,8,10 24,7,11 25,12,15 26,5,10 27,10,13 28,15,19 29,9,12 30,9,9 31,9,14 32,8,10 33,9,11 34,8,9 35,9,14 36,13,14 37,6,7 38,15,16 39,11,13 40,6,8 41,8,8 42,13,14 43,7,10 44,5,5 45,7,7 46,9,9 47,9,9 48,22,22 49,6,7 50,10,10 51,6,6 52,13,14 53,8,8 54,7,7 55,13,13 56,11,11 57,8,8 58,8,8 59,9,10 60,13,16 61,5,5 62,5,6 63,5,5 64,5,5 65,10,10 66,8,8 67,4,4 68,5,5 69,4,5 70,8,8 71,0,0 72,9,9 73,1,1 74,4,4 75,7,7 76,6,6 77,2,2 78,3,3 79,2,2 80,4,4 81,1,1 82,1,1 83,2,2 84,0,0 85,0,0 86,1,1 PKTSMo_C11pygam/datasets/load_datasets.py""" GAM datasets """ # -*- coding: utf-8 -*- from os.path import dirname import pandas as pd import numpy as np from pygam.utils import make_2d PATH = dirname(__file__) def _clean_X_y(X, y): """ensure that X and y data are float and correct shapes """ return make_2d(X, verbose=False).astype('float'), y.astype('float') def mcycle(return_X_y=True): """motorcyle acceleration dataset Parameters ---------- return_X_y : bool, if True, returns a model-ready tuple of data (X, y) otherwise, returns a Pandas DataFrame Returns ------- model-ready tuple of data (X, y) OR Pandas DataFrame Notes ----- X contains the times after the impact. y contains the acceleration. Source: https://vincentarelbundock.github.io/Rdatasets/doc/MASS/mcycle.html """ # y is real # recommend LinearGAM motor = pd.read_csv(PATH + '/mcycle.csv', index_col=0) if return_X_y: X = motor.times.values y = motor.accel return _clean_X_y(X, y) return motor def coal(return_X_y=True): """coal-mining accidents dataset Parameters ---------- return_X_y : bool, if True, returns a model-ready tuple of data (X, y) otherwise, returns a Pandas DataFrame Returns ------- model-ready tuple of data (X, y) OR Pandas DataFrame Notes ----- The (X, y) tuple is a processed version of the otherwise raw DataFrame. A histogram of 150 bins has been computed describing the number accidents per year. X contains the midpoints of histogram bins. y contains the count in each histogram bin. Source: https://vincentarelbundock.github.io/Rdatasets/doc/boot/coal.html """ # y is counts # recommend PoissonGAM coal = pd.read_csv(PATH + '/coal.csv', index_col=0) if return_X_y: y, x = np.histogram(coal.values, bins=150) X = x[:-1] + np.diff(x)/2 # get midpoints of bins return _clean_X_y(X, y) return coal def faithful(return_X_y=True): """old-faithful dataset Parameters ---------- return_X_y : bool, if True, returns a model-ready tuple of data (X, y) otherwise, returns a Pandas DataFrame Returns ------- model-ready tuple of data (X, y) OR Pandas DataFrame Notes ----- The (X, y) tuple is a processed version of the otherwise raw DataFrame. A histogram of 200 bins has been computed describing the wating time between eruptions. X contains the midpoints of histogram bins. y contains the count in each histogram bin. Source: https://vincentarelbundock.github.io/Rdatasets/doc/datasets/faithful.html """ # y is counts # recommend PoissonGAM faithful = pd.read_csv(PATH + '/faithful.csv', index_col=0) if return_X_y: y, x = np.histogram(faithful['eruptions'], bins=200) X = x[:-1] + np.diff(x)/2 # get midpoints of bins return _clean_X_y(X, y) return faithful def wage(return_X_y=True): """wage dataset Parameters ---------- return_X_y : bool, if True, returns a model-ready tuple of data (X, y) otherwise, returns a Pandas DataFrame Returns ------- model-ready tuple of data (X, y) OR Pandas DataFrame Notes ----- X contains the year, age and education of each sampled person. The education category has been transformed to integers. y contains the wage. Source: https://github.com/JWarmenhoven/ISLR-python/blob/master/Notebooks/Data/Wage.csv """ # y is real # recommend LinearGAM wage = pd.read_csv(PATH + '/wage.csv', index_col=0) if return_X_y: X = wage[['year', 'age', 'education']].values X[:,-1] = np.unique(X[:,-1], return_inverse=True)[1] y = wage['wage'].values return _clean_X_y(X, y) return wage def trees(return_X_y=True): """cherry trees dataset Parameters ---------- return_X_y : bool, if True, returns a model-ready tuple of data (X, y) otherwise, returns a Pandas DataFrame Returns ------- model-ready tuple of data (X, y) OR Pandas DataFrame Notes ----- X contains the girth and the height of each tree. y contains the volume. Source: https://vincentarelbundock.github.io/Rdatasets/doc/datasets/trees.html """ # y is real. # recommend InvGaussGAM, or GAM(distribution='gamma', link='log') trees = pd.read_csv(PATH + '/trees.csv', index_col=0) if return_X_y: y = trees.Volume.values X = trees[['Girth', 'Height']].values return _clean_X_y(X, y) return trees def default(return_X_y=True): """credit default dataset Parameters ---------- return_X_y : bool, if True, returns a model-ready tuple of data (X, y) otherwise, returns a Pandas DataFrame Returns ------- model-ready tuple of data (X, y) OR Pandas DataFrame Notes ----- X contains the category of student or not, credit card balance, and income. y contains the outcome of default (0) or not (1). Source: https://vincentarelbundock.github.io/Rdatasets/doc/ISLR/Default.html """ # y is binary # recommend LogisticGAM default = pd.read_csv(PATH + '/default.csv', index_col=0) if return_X_y: default = default.values default[:,0] = np.unique(default[:,0], return_inverse=True)[1] default[:,1] = np.unique(default[:,1], return_inverse=True)[1] X = default[:,1:] y = default[:,0] return _clean_X_y(X, y) return default def cake(return_X_y=True): """cake dataset Parameters ---------- return_X_y : bool, if True, returns a model-ready tuple of data (X, y) otherwise, returns a Pandas DataFrame Returns ------- model-ready tuple of data (X, y) OR Pandas DataFrame Notes ----- X contains the category of recipe used transformed to an integer, the catergory of replicate, and the temperatue. y contains the angle at which the cake broke. Source: https://vincentarelbundock.github.io/Rdatasets/doc/lme4/cake.html """ # y is real # recommend LinearGAM cake = pd.read_csv(PATH + '/cake.csv', index_col=0) if return_X_y: X = cake[['recipe', 'replicate', 'temperature']].values X[:,0] = np.unique(cake.values[:,1], return_inverse=True)[1] X[:,1] -= 1 y = cake['angle'].values return _clean_X_y(X, y) return cake def hepatitis(return_X_y=True): """hepatitis in Bulgaria dataset Parameters ---------- return_X_y : bool, if True, returns a model-ready tuple of data (X, y) otherwise, returns a Pandas DataFrame Returns ------- model-ready tuple of data (X, y) OR Pandas DataFrame Notes ----- X contains the age of each patient group. y contains the ratio of HAV positive patients to the total number for each age group. Groups with 0 total patients are excluded. Source: Keiding, N. (1991) Age-specific incidence and prevalence: a statistical perspective """ # y is real # recommend LinearGAM hep = pd.read_csv(PATH + '/hepatitis_A_bulgaria.csv').astype(float) if return_X_y: # eliminate 0/0 mask = (hep.total > 0).values hep = hep[mask] X = hep.age.values y = hep.hepatitis_A_positive.values / hep.total.values return _clean_X_y(X, y) return hep def toy_classification(return_X_y=True, n=5000): """toy classification dataset with irrelevant features fitting a logistic model on this data and performing a model summary should reveal that features 2,3,4 are not significant. Parameters ---------- return_X_y : bool, if True, returns a model-ready tuple of data (X, y) otherwise, returns a Pandas DataFrame n : int, default: 5000 number of samples to generate Returns ------- model-ready tuple of data (X, y) OR Pandas DataFrame Notes ----- X contains 5 variables: continuous feature 0 continuous feature 1 irrelevant feature 0 irrelevant feature 1 irrelevant feature 2 categorical feature 0 y contains binary labels Also, this dataset is randomly generated and will vary each time. """ # make features X = np.random.rand(n,5) * 10 - 5 cat = np.random.randint(0,4, n) X = np.c_[X, cat] # make observations log_odds = (-0.5*X[:,0]**2) + 5 +(-0.5*X[:,1]**2) + np.mod(X[:,-1], 2)*-30 p = 1/(1+np.exp(-log_odds)).squeeze() y = (np.random.rand(n) < p).astype(np.int) if return_X_y: return X, y else: return pd.DataFrame(np.c_[X, y], columns=[['continuous0', 'continuous1', 'irrelevant0', 'irrelevant1', 'irrelevant2', 'categorical0', 'observations' ]]) def head_circumference(return_X_y=True): """head circumference for dutch boys Parameters ---------- return_X_y : bool, if True, returns a model-ready tuple of data (X, y) otherwise, returns a Pandas DataFrame Returns ------- model-ready tuple of data (X, y) OR Pandas DataFrame Notes ----- X contains the age in years of each patient. y contains the head circumference in centimeters """ # y is real # recommend ExpectileGAM head = pd.read_csv(PATH + '/head_circumference.csv', index_col=0).astype(float) if return_X_y: y = head['head'].values X = head[['age']].values return _clean_X_y(X, y) return head def chicago(return_X_y=True): """Chicago air pollution and death rate data Parameters ---------- return_X_y : bool, if True, returns a model-ready tuple of data (X, y) otherwise, returns a Pandas DataFrame Returns ------- model-ready tuple of data (X, y) OR Pandas DataFrame Notes ----- X contains [['time', 'tmpd', 'pm10median', 'o3median']], with no NaNs y contains 'death', the deaths per day, with no NaNs Source: R gamair package `data(chicago)` Notes ----- https://cran.r-project.org/web/packages/gamair/gamair.pdf https://rdrr.io/cran/gamair/man/chicago.html Columns: death : total deaths (per day). pm10median : median particles in 2.5-10 per cubic m pm25median : median particles < 2.5 mg per cubic m (more dangerous). o3median : Ozone in parts per billion so2median : Median Sulpher dioxide measurement time : time in days tmpd : temperature in fahrenheit """ # recommend PoissonGAM chi = pd.read_csv(PATH + '/chicago.csv', index_col=0).astype(float) if return_X_y: chi = chi[['time', 'tmpd', 'pm10median', 'o3median', 'death']].dropna() X = chi[['time', 'tmpd', 'pm10median', 'o3median']].values y = chi['death'].values return X, y else: return chi def toy_interaction(return_X_y=True, n=50000, stddev=0.1): """a sinusoid modulated by a linear function this is a simple dataset to test a model's capacity to fit interactions between features. a GAM with no interaction terms will have an R-squared close to 0, while a GAM with a tensor product will have R-squared close to 1. the data is random, and will vary on each invocation. Parameters ---------- return_X_y : bool, if True, returns a model-ready tuple of data (X, y) otherwise, returns a Pandas DataFrame n : int, optional number of points to generate stddev : positive float, optional, standard deviation of irreducible error Returns ------- model-ready tuple of data (X, y) OR Pandas DataFrame Notes ----- X contains [['sinusoid', 'linear']] y is formed by multiplying the sinusoid by the linear function. Source: """ X = np.random.uniform(-1,1, size=(n, 2)) X[:, 1] *= 5 y = np.sin(X[:,0] * 2 * np.pi * 1.5) * X[:,1] y += np.random.randn(len(X)) * stddev if return_X_y: return X, y else: data = pd.DataFrame(np.c_[X, y]) data.columns = [['sinusoid', 'linear', 'y']] return data PKIM"Ipygam/datasets/mcycle.csv"","times","accel" "1",2.4,0 "2",2.6,-1.3 "3",3.2,-2.7 "4",3.6,0 "5",4,-2.7 "6",6.2,-2.7 "7",6.6,-2.7 "8",6.8,-1.3 "9",7.8,-2.7 "10",8.2,-2.7 "11",8.8,-1.3 "12",8.8,-2.7 "13",9.6,-2.7 "14",10,-2.7 "15",10.2,-5.4 "16",10.6,-2.7 "17",11,-5.4 "18",11.4,0 "19",13.2,-2.7 "20",13.6,-2.7 "21",13.8,0 "22",14.6,-13.3 "23",14.6,-5.4 "24",14.6,-5.4 "25",14.6,-9.3 "26",14.6,-16 "27",14.6,-22.8 "28",14.8,-2.7 "29",15.4,-22.8 "30",15.4,-32.1 "31",15.4,-53.5 "32",15.4,-54.9 "33",15.6,-40.2 "34",15.6,-21.5 "35",15.8,-21.5 "36",15.8,-50.8 "37",16,-42.9 "38",16,-26.8 "39",16.2,-21.5 "40",16.2,-50.8 "41",16.2,-61.7 "42",16.4,-5.4 "43",16.4,-80.4 "44",16.6,-59 "45",16.8,-71 "46",16.8,-91.1 "47",16.8,-77.7 "48",17.6,-37.5 "49",17.6,-85.6 "50",17.6,-123.1 "51",17.6,-101.9 "52",17.8,-99.1 "53",17.8,-104.4 "54",18.6,-112.5 "55",18.6,-50.8 "56",19.2,-123.1 "57",19.4,-85.6 "58",19.4,-72.3 "59",19.6,-127.2 "60",20.2,-123.1 "61",20.4,-117.9 "62",21.2,-134 "63",21.4,-101.9 "64",21.8,-108.4 "65",22,-123.1 "66",23.2,-123.1 "67",23.4,-128.5 "68",24,-112.5 "69",24.2,-95.1 "70",24.2,-81.8 "71",24.6,-53.5 "72",25,-64.4 "73",25,-57.6 "74",25.4,-72.3 "75",25.4,-44.3 "76",25.6,-26.8 "77",26,-5.4 "78",26.2,-107.1 "79",26.2,-21.5 "80",26.4,-65.6 "81",27,-16 "82",27.2,-45.6 "83",27.2,-24.2 "84",27.2,9.5 "85",27.6,4 "86",28.2,12 "87",28.4,-21.5 "88",28.4,37.5 "89",28.6,46.9 "90",29.4,-17.4 "91",30.2,36.2 "92",31,75 "93",31.2,8.1 "94",32,54.9 "95",32,48.2 "96",32.8,46.9 "97",33.4,16 "98",33.8,45.6 "99",34.4,1.3 "100",34.8,75 "101",35.2,-16 "102",35.2,-54.9 "103",35.4,69.6 "104",35.6,34.8 "105",35.6,32.1 "106",36.2,-37.5 "107",36.2,22.8 "108",38,46.9 "109",38,10.7 "110",39.2,5.4 "111",39.4,-1.3 "112",40,-21.5 "113",40.4,-13.3 "114",41.6,30.8 "115",41.6,-10.7 "116",42.4,29.4 "117",42.8,0 "118",42.8,-10.7 "119",43,14.7 "120",44,-1.3 "121",44.4,0 "122",45,10.7 "123",46.6,10.7 "124",47.8,-26.8 "125",47.8,-14.7 "126",48.8,-13.3 "127",50.6,0 "128",52,10.7 "129",53.2,-14.7 "130",55,-2.7 "131",55,10.7 "132",55.4,-2.7 "133",57.6,10.7 PKIM6++pygam/datasets/trees.csv"","Girth","Height","Volume" "1",8.3,70,10.3 "2",8.6,65,10.3 "3",8.8,63,10.2 "4",10.5,72,16.4 "5",10.7,81,18.8 "6",10.8,83,19.7 "7",11,66,15.6 "8",11,75,18.2 "9",11.1,80,22.6 "10",11.2,75,19.9 "11",11.3,79,24.2 "12",11.4,76,21 "13",11.4,76,21.4 "14",11.7,69,21.3 "15",12,75,19.1 "16",12.9,74,22.2 "17",12.9,85,33.8 "18",13.3,86,27.4 "19",13.7,71,25.7 "20",13.8,64,24.9 "21",14,78,34.5 "22",14.2,80,31.7 "23",14.5,74,36.3 "24",16,72,38.3 "25",16.3,77,42.6 "26",17.3,81,55.4 "27",17.5,82,55.7 "28",17.9,80,58.3 "29",18,80,51.5 "30",18,80,51 "31",20.6,87,77 PKIMP\^~^~pygam/datasets/wage.csv"","year","age","sex","maritl","race","education","region","jobclass","health","health_ins","logwage","wage" "231655",2006,18,"1. Male","1. Never Married","1. White","1. < HS Grad","2. Middle Atlantic","1. Industrial","1. <=Good","2. No",4.31806333496276,75.0431540173515 "86582",2004,24,"1. Male","1. Never Married","1. White","4. College Grad","2. Middle Atlantic","2. Information","2. >=Very Good","2. No",4.25527250510331,70.4760196469445 "161300",2003,45,"1. Male","2. Married","1. White","3. Some College","2. Middle Atlantic","1. Industrial","1. <=Good","1. Yes",4.8750612633917,130.982177377461 "155159",2003,43,"1. Male","2. Married","3. Asian","4. College Grad","2. Middle Atlantic","2. Information","2. >=Very Good","1. Yes",5.04139268515823,154.68529299563 "11443",2005,50,"1. Male","4. Divorced","1. White","2. HS Grad","2. Middle Atlantic","2. Information","1. <=Good","1. Yes",4.31806333496276,75.0431540173515 "376662",2008,54,"1. Male","2. Married","1. White","4. College Grad","2. Middle Atlantic","2. Information","2. >=Very Good","1. Yes",4.84509804001426,127.115743812184 "450601",2009,44,"1. Male","2. Married","4. Other","3. Some College","2. Middle Atlantic","1. Industrial","2. >=Very Good","1. Yes",5.13302127864665,169.528538036679 "377954",2008,30,"1. Male","1. Never Married","3. Asian","3. Some College","2. Middle Atlantic","2. Information","1. <=Good","1. Yes",4.7160033436348,111.720849360989 "228963",2006,41,"1. Male","1. Never Married","2. Black","3. Some College","2. Middle Atlantic","2. Information","2. >=Very Good","1. Yes",4.77815125038364,118.884359339886 "81404",2004,52,"1. Male","2. Married","1. White","2. HS Grad","2. Middle Atlantic","2. Information","2. >=Very Good","1. Yes",4.85733249643127,128.680488220624 "302778",2007,45,"1. Male","4. Divorced","1. White","3. Some College","2. Middle Atlantic","2. Information","1. <=Good","1. Yes",4.76342799356294,117.146816914805 "305706",2007,34,"1. Male","2. Married","1. White","2. HS Grad","2. Middle Atlantic","1. Industrial","2. >=Very Good","2. No",4.39794000867204,81.2832532842527 "8690",2005,35,"1. Male","1. Never Married","1. White","2. HS Grad","2. Middle Atlantic","2. Information","2. >=Very Good","1. Yes",4.49415459401844,89.4924795180001 "153561",2003,39,"1. Male","2. Married","1. White","4. College Grad","2. Middle Atlantic","1. Industrial","2. >=Very Good","1. Yes",4.90308998699194,134.705375118879 "449654",2009,54,"1. Male","2. Married","1. White","2. HS Grad","2. Middle Atlantic","2. Information","2. >=Very Good","1. Yes",4.90308998699194,134.705375118879 "447660",2009,51,"1. Male","2. Married","1. White","3. Some College","2. Middle Atlantic","1. Industrial","2. >=Very Good","1. Yes",4.50514997831991,90.4819133566401 "160191",2003,37,"1. Male","1. Never Married","3. Asian","4. College Grad","2. Middle Atlantic","1. Industrial","2. >=Very Good","2. No",4.41497334797082,82.6796372966372 "230312",2006,50,"1. Male","2. Married","1. White","5. Advanced Degree","2. Middle Atlantic","2. Information","2. >=Very Good","2. No",5.36055176170483,212.842352315711 "301585",2007,56,"1. 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Yes",4.50514997831991,90.4819133566401 PKIMpygam/tests/__init__.pyPKTSMA"pygam/tests/conftest.py# -*- coding: utf-8 -*- import pytest import pandas as pd import numpy as np from pygam import * from pygam.datasets import (mcycle, coal, faithful, cake, coal, default, trees, hepatitis, wage, toy_classification, head_circumference, chicago, toy_interaction) @pytest.fixture def mcycle_X_y(): # y is real # recommend LinearGAM return mcycle(return_X_y=True) @pytest.fixture def mcycle_gam(mcycle_X_y): X, y = mcycle_X_y gam = LinearGAM().fit(X,y) return gam @pytest.fixture def coal_X_y(): # y is counts # recommend PoissonGAM return coal(return_X_y=True) @pytest.fixture def faithful_X_y(): # y is counts # recommend PoissonGAM return faithful(return_X_y=True) @pytest.fixture def wage_X_y(): # y is real # recommend LinearGAM return wage(return_X_y=True) @pytest.fixture def wage_gam(wage_X_y): X, y = wage_X_y gam = LinearGAM(s(0) + s(1) + f(2)).fit(X, y) return gam @pytest.fixture def trees_X_y(): # y is real. # recommend InvGaussGAM, or GAM(distribution='gamma', link='log') return trees(return_X_y=True) @pytest.fixture def default_X_y(): # y is binary # recommend LogisticGAM return default(return_X_y=True) @pytest.fixture def cake_X_y(): # y is real # recommend LinearGAM return cake(return_X_y=True) @pytest.fixture def hepatitis_X_y(): # y is real # recommend LinearGAM return hepatitis(return_X_y=True) @pytest.fixture def toy_classification_X_y(): # y is binary ints # recommend LogisticGAM return toy_classification(return_X_y=True) @pytest.fixture def head_circumference_X_y(): # centile data # recommend ExpectileGAM return head_circumference(return_X_y=True) @pytest.fixture def chicago_X_y(): # y is counts # recommend PoissonGAM return chicago(return_X_y=True) @pytest.fixture def chicago_gam(chicago_X_y): X, y = chicago_X_y gam = PoissonGAM(terms=s(0, n_splines=200) + te(3, 1) + s(2)).fit(X, y) return gam @pytest.fixture def toy_interaction_X_y(): # y is real # recommend LinearGAM return toy_interaction(return_X_y=True) PK•YM;RGGpygam/tests/test_GAM_methods.py# -*- coding: utf-8 -*- import sys import numpy as np import pytest import scipy as sp from pygam import * def test_LinearGAM_prediction(mcycle_X_y, mcycle_gam): """ check that we the predictions we get are correct shape """ X, y = mcycle_X_y preds = mcycle_gam.predict(X) assert(preds.shape == y.shape) def test_LogisticGAM_accuracy(default_X_y): """ check that we can compute accuracy correctly """ X, y = default_X_y gam = LogisticGAM().fit(X, y) preds = gam.predict(X) acc0 = (preds == y).mean() acc1 = gam.accuracy(X, y) assert(acc0 == acc1) def test_PoissonGAM_exposure(coal_X_y): """ check that we can fit a Poisson GAM with exposure, and it scales predictions """ X, y = coal_X_y gam = PoissonGAM().fit(X, y, exposure=np.ones_like(y)) assert((gam.predict(X, exposure=np.ones_like(y)*2) == 2 *gam.predict(X)).all()) def test_PoissonGAM_loglike(coal_X_y): """ check that our loglikelihood is scaled by exposure predictions that are twice as large with twice the exposure should have lower loglikelihood """ X, y = coal_X_y exposure = np.ones_like(y) gam_high_var = PoissonGAM().fit(X, y * 2, exposure=exposure * 2) gam_low_var = PoissonGAM().fit(X, y, exposure=exposure) assert gam_high_var.loglikelihood(X, y * 2, exposure * 2) < gam_low_var.loglikelihood(X, y, exposure) def test_large_GAM(coal_X_y): """ check that we can fit a GAM in py3 when we have more than 50,000 samples """ X = np.linspace(0, 100, 100000) y = X**2 gam = LinearGAM().fit(X, y) assert(gam._is_fitted) def test_summary(mcycle_X_y, mcycle_gam): """ check that we can get a summary if we've fitted the model, else not """ X, y = mcycle_X_y gam = LinearGAM() try: gam.summary() except AttributeError: assert(True) mcycle_gam.summary() assert(True) def test_more_splines_than_samples(mcycle_X_y): """ check that gridsearch returns the expected number of models """ X, y = mcycle_X_y n = len(X) gam = LinearGAM(s(0, n_splines=n+1)).fit(X, y) assert(gam._is_fitted) # TODO here is our bug: # we cannot display the term-by-term effective DoF because we have fewer # values than coefficients assert len(gam.statistics_['edof_per_coef']) < len(gam.coef_) gam.summary() def test_deviance_residuals(mcycle_X_y, mcycle_gam): """ for linear GAMs, the deviance residuals should be equal to the y - y_pred """ X, y = mcycle_X_y res = mcycle_gam.deviance_residuals(X, y) err = y - mcycle_gam.predict(X) assert((res == err).all()) def test_conf_intervals_return_array(mcycle_X_y, mcycle_gam): """ make sure that the confidence_intervals method returns an array """ X, y = mcycle_X_y conf_ints = mcycle_gam.confidence_intervals(X) assert(conf_ints.ndim == 2) def test_conf_intervals_quantiles_width_interchangable(mcycle_X_y, mcycle_gam): """ getting confidence_intervals via width or specifying quantiles should return the same result """ X, y = mcycle_X_y conf_ints_a = mcycle_gam.confidence_intervals(X, width=.9) conf_ints_b = mcycle_gam.confidence_intervals(X, quantiles=[.05, .95]) assert(np.allclose(conf_ints_a, conf_ints_b)) def test_conf_intervals_ordered(mcycle_X_y, mcycle_gam): """ comfidence intervals returned via width should be ordered """ X, y = mcycle_X_y conf_ints = mcycle_gam.confidence_intervals(X) assert((conf_ints[:,0] <= conf_ints[:,1]).all()) def test_summary_returns_12_lines(mcycle_gam): """ check that the summary method works and returns 24 lines like: LinearGAM =============================================== ========================================================== Distribution: NormalDist Effective DoF: 11.2495 Link Function: IdentityLink Log Likelihood: -952.605 Number of Samples: 133 AIC: 1929.7091 AICc: 1932.4197 GCV: 605.6546 Scale: 514.2013 Pseudo R-Squared: 0.7969 ========================================================================================================== Feature Function Data Type Num Splines Spline Order Linear Fit Lambda P > x Sig. Code ================== ============== ============= ============= =========== ========== ========== ========== feature 1 numerical 25 3 False 1.0 3.43e-03 ** intercept 6.85e-02 . ========================================================================================================== Significance codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 WARNING: Fitting splines and a linear function to a feature introduces a model identifiability problem which can cause p-values to appear significant when they are not. WARNING: p-values calculated in this manner behave correctly for un-penalized models or models with known smoothing parameters, but when smoothing parameters have been estimated, the p-values are typically lower than they should be, meaning that the tests reject the null too readily. """ if sys.version_info.major == 2: from StringIO import StringIO if sys.version_info.major == 3: from io import StringIO stdout = sys.stdout #keep a handle on the real standard output sys.stdout = StringIO() #Choose a file-like object to write to mcycle_gam.summary() assert(len(sys.stdout.getvalue().split('\n')) == 24) def test_is_fitted_predict(mcycle_X_y): """ test predict requires fitted model """ X, y = mcycle_X_y gam = LinearGAM() with pytest.raises(AttributeError): gam.predict(X) def test_is_fitted_predict_mu(mcycle_X_y): """ test predict_mu requires fitted model """ X, y = mcycle_X_y gam = LinearGAM() with pytest.raises(AttributeError): gam.predict_mu(X) def test_is_fitted_dev_resid(mcycle_X_y): """ test deviance_residuals requires fitted model """ X, y = mcycle_X_y gam = LinearGAM() with pytest.raises(AttributeError): gam.deviance_residuals(X, y) def test_is_fitted_conf_intervals(mcycle_X_y): """ test confidence_intervals requires fitted model """ X, y = mcycle_X_y gam = LinearGAM() with pytest.raises(AttributeError): gam.confidence_intervals(X) def test_is_fitted_pdep(mcycle_X_y): """ test partial_dependence requires fitted model """ gam = LinearGAM() with pytest.raises(AttributeError): gam.partial_dependence(term=0) def test_is_fitted_summary(mcycle_X_y): """ test summary requires fitted model """ X, y = mcycle_X_y gam = LinearGAM() with pytest.raises(AttributeError): gam.summary() def test_set_params_with_external_param(): """ test set_params sets a real parameter """ gam = GAM(lam=1) gam.set_params(lam=420) assert(gam.lam == 420) def test_set_params_with_phony_param(): """ test set_params should not set any phony param """ gam = GAM() gam.set_params(cat=420) assert(not hasattr(gam, 'cat')) def test_set_params_with_phony_param_force(): """ test set_params can set phony params if we use the force=True """ gam = GAM() assert(not hasattr(gam, 'cat')) gam.set_params(cat=420, force=True) assert(gam.cat == 420) def test_get_params(): """ test gam gets our params """ gam = GAM(lam=420) params = gam.get_params() assert(params['lam'] == 420) class TestSamplingFromPosterior(object): def test_drawing_samples_from_unfitted_model(self, mcycle_X_y, mcycle_gam): X, y = mcycle_X_y gam = LinearGAM() with pytest.raises(AttributeError): gam.sample(X, y) with pytest.raises(AttributeError): gam._sample_coef(X, y) with pytest.raises(AttributeError): gam._bootstrap_samples_of_smoothing(X, y) assert mcycle_gam._is_fitted mcycle_gam.sample(X, y, n_draws=2) mcycle_gam._sample_coef(X, y, n_draws=2) mcycle_gam._bootstrap_samples_of_smoothing(X, y, n_bootstraps=1) assert True def test_sample_quantity(self, mcycle_X_y, mcycle_gam): X, y = mcycle_X_y for quantity in ['coefficients', 'response']: with pytest.raises(ValueError): mcycle_gam.sample(X, y, quantity=quantity, n_draws=2) for quantity in ['coef', 'mu', 'y']: mcycle_gam.sample(X, y, quantity=quantity, n_draws=2) assert True def test_shape_of_random_samples(self, mcycle_X_y, mcycle_gam): X, y = mcycle_X_y n_samples = len(X) n_draws = 5 sample_coef = mcycle_gam.sample(X, y, quantity='coef', n_draws=n_draws) sample_mu = mcycle_gam.sample(X, y, quantity='mu', n_draws=n_draws) sample_y = mcycle_gam.sample(X, y, quantity='y', n_draws=n_draws) assert sample_coef.shape == (n_draws, len(mcycle_gam.coef_)) assert sample_mu.shape == (n_draws, n_samples) assert sample_y.shape == (n_draws, n_samples) n_samples_in_grid = 500 idxs = np.random.choice(np.arange(len(X)), n_samples_in_grid) XX = X[idxs] sample_coef = mcycle_gam.sample(X, y, quantity='coef', n_draws=n_draws, sample_at_X=XX) sample_mu = mcycle_gam.sample(X, y, quantity='mu', n_draws=n_draws, sample_at_X=XX) sample_y = mcycle_gam.sample(X, y, quantity='y', n_draws=n_draws, sample_at_X=XX) assert sample_coef.shape == (n_draws, len(mcycle_gam.coef_)) assert sample_mu.shape == (n_draws, n_samples_in_grid) assert sample_y.shape == (n_draws, n_samples_in_grid) def test_shape_bootstrap_samples_of_smoothing(self, mcycle_X_y, mcycle_gam): X, y = mcycle_X_y for n_bootstraps in [1, 2]: coef_bootstraps, cov_bootstraps = ( mcycle_gam._bootstrap_samples_of_smoothing( X, y, n_bootstraps=n_bootstraps)) assert len(coef_bootstraps) == len(cov_bootstraps) == n_bootstraps for coef, cov in zip(coef_bootstraps, cov_bootstraps): assert coef.shape == mcycle_gam.coef_.shape assert cov.shape == mcycle_gam.statistics_['cov'].shape for n_draws in [1, 2]: coef_draws = mcycle_gam._simulate_coef_from_bootstraps( n_draws, coef_bootstraps, cov_bootstraps) assert coef_draws.shape == (n_draws, len(mcycle_gam.coef_)) def test_bad_sample_params(self, mcycle_X_y, mcycle_gam): X, y = mcycle_X_y with pytest.raises(ValueError): mcycle_gam.sample(X, y, n_draws=0) with pytest.raises(ValueError): mcycle_gam.sample(X, y, n_bootstraps=0) def test_prediction_interval_unknown_scale(): """ the prediction intervals should be correct to a few decimal places we test at a large sample limit, where the t distribution becomes normal """ n = 1000000 X = np.linspace(0,1,n) y = np.random.randn(n) gam_a = LinearGAM(terms=l(0)).fit(X, y) gam_b = LinearGAM(s(0, n_splines=4)).fit(X, y) XX = gam_a.generate_X_grid(term=0) intervals_a = gam_a.prediction_intervals(XX, quantiles=[0.1, .9]).mean(axis=0) intervals_b = gam_b.prediction_intervals(XX, quantiles=[0.1, .9]).mean(axis=0) assert np.allclose(intervals_a[0], sp.stats.norm.ppf(0.1), atol=0.01) assert np.allclose(intervals_a[1], sp.stats.norm.ppf(0.9), atol=0.01) assert np.allclose(intervals_b[0], sp.stats.norm.ppf(0.1), atol=0.01) assert np.allclose(intervals_b[1], sp.stats.norm.ppf(0.9), atol=0.01) def test_prediction_interval_known_scale(): """ the prediction intervals should be correct to a few decimal places we test at a large sample limit. """ n = 1000000 X = np.linspace(0,1,n) y = np.random.randn(n) gam_a = LinearGAM(terms=l(0), scale=1.).fit(X, y) gam_b = LinearGAM(s(0, n_splines=4), scale=1.).fit(X, y) XX = gam_a.generate_X_grid(term=0) intervals_a = gam_a.prediction_intervals(XX, quantiles=[0.1, .9]).mean(axis=0) intervals_b = gam_b.prediction_intervals(XX, quantiles=[0.1, .9]).mean(axis=0) assert np.allclose(intervals_a[0], sp.stats.norm.ppf(0.1), atol=0.01) assert np.allclose(intervals_a[1], sp.stats.norm.ppf(0.9), atol=0.01) assert np.allclose(intervals_b[0], sp.stats.norm.ppf(0.1), atol=0.01) assert np.allclose(intervals_b[1], sp.stats.norm.ppf(0.9), atol=0.01) def test_pvalue_rejects_useless_feature(wage_X_y): """ check that a p-value can reject a useless feature """ X, y = wage_X_y # add empty feature X = np.c_[X, np.arange(X.shape[0])] gam = LinearGAM(s(0) + s(1) + f(2) + s(3)).fit(X, y) # now do the test, with some safety p_values = gam._estimate_p_values() print(p_values) assert(p_values[-2] > .5) # because -1 is intercept def test_fit_quantile_is_close_enough(head_circumference_X_y): """see that we get close to the desired quantile and check that repeating on an already fitted returns the same """ X, y = head_circumference_X_y quantile = 0.99 tol = 1e-4 gam = ExpectileGAM().fit_quantile(X, y, quantile=quantile, max_iter=20, tol=tol) ratio = gam._get_quantile_ratio(X, y) assert np.abs(ratio - quantile) <= tol # now check if we had to refit gam2 = gam.fit_quantile(X, y, quantile=quantile, max_iter=20, tol=tol) assert gam == gam2 def test_fit_quantile_NOT_close_enough(head_circumference_X_y): """see that we DO NOT get close to the desired quantile """ X, y = head_circumference_X_y quantile = 0.99 tol = 1e-5 gam = ExpectileGAM().fit_quantile(X, y, quantile=quantile, max_iter=1, tol=tol) ratio = gam._get_quantile_ratio(X, y) assert np.abs(ratio - quantile) > tol def test_fit_quantile_raises_ValueError(head_circumference_X_y): """see that we DO NOT get fit on bad argument requests """ X, y = head_circumference_X_y with pytest.raises(ValueError): ExpectileGAM().fit_quantile(X, y, quantile=0) with pytest.raises(ValueError): ExpectileGAM().fit_quantile(X, y, quantile=1) with pytest.raises(ValueError): ExpectileGAM().fit_quantile(X, y, quantile=-0.1) with pytest.raises(ValueError): ExpectileGAM().fit_quantile(X, y, quantile=1.1) with pytest.raises(ValueError): ExpectileGAM().fit_quantile(X, y, tol=0, quantile=0.5) with pytest.raises(ValueError): ExpectileGAM().fit_quantile(X, y, tol=-0.1, quantile=0.5) with pytest.raises(ValueError): ExpectileGAM().fit_quantile(X, y, max_iter=0, quantile=0.5) with pytest.raises(ValueError): ExpectileGAM().fit_quantile(X, y, max_iter=-1, quantile=0.5) class TestRegressions(object): def test_pvalue_invariant_to_scale(self, wage_X_y): """ regression test. a bug made the F-statistic sensitive to scale changes, when it should be invariant. check that a p-value should not change when we change the scale of the response """ X, y = wage_X_y gamA = LinearGAM(s(0) + s(1) + f(2)).fit(X, y * 1000000) gamB = LinearGAM(s(0) + s(1) + f(2)).fit(X, y) assert np.allclose(gamA.statistics_['p_values'], gamB.statistics_['p_values']) def test_2d_y_still_allow_fitting_in_PoissonGAM(self, coal_X_y): """ regression test. there was a bug where we forgot to check the y_array before converting exposure to weights. """ X, y = coal_X_y two_d_data = np.ones_like(y).ravel()[:, None] # 2d y should cause no problems now gam = PoissonGAM().fit(X, y[:, None]) assert gam._is_fitted # 2d weghts should cause no problems now gam = PoissonGAM().fit(X, y, weights=two_d_data) assert gam._is_fitted # 2d exposure should cause no problems now gam = PoissonGAM().fit(X, y, exposure=two_d_data) assert gam._is_fitted def test_non_int_exposure_produced_no_inf_in_PoissonGAM_ll(self, coal_X_y): """ regression test. there was a bug where we forgot to round the rescaled counts before computing the loglikelihood. since Poisson requires integer observations, small numerical errors caused the pmf to return -inf, which shows up in the loglikelihood computations, AIC, AICc.. """ X, y = coal_X_y rate = 1.2 + np.cos(np.linspace(0, 2. * np.pi, len(y))) gam = PoissonGAM().fit(X, y, exposure=rate) assert np.isfinite(gam.statistics_['loglikelihood']) def test_initial_estimate_runs_for_int_obseravtions(self, toy_classification_X_y): """ regression test ._initial_estimate would fail when trying to add small numbers to integer observations casting the observations to float in that method fixes that """ X, y = toy_classification_X_y gam = LogisticGAM().fit(X, y) assert gam._is_fitted def test_r_squared_for_new_dataset(self, mcycle_gam, mcycle_X_y): """ regression test estimate r squared used to refer to a non-existant method when `mu=None` """ X, y = mcycle_X_y mcycle_gam._estimate_r2(X, y) PKTSMUl pygam/tests/test_GAM_params.py# -*- coding: utf-8 -*- import numpy as np import pytest from pygam import * def test_lam_non_neg_array_like(cake_X_y): """ lambda must be a non-negative float or array of floats """ X, y = cake_X_y try: gam = LinearGAM(lam=-1).fit(X, y) except ValueError: assert(True) try: gam = LinearGAM(lam=['hi']).fit(X, y) except ValueError: assert(True) def test_penalties_must_be_or_contain_callable_or_auto(mcycle_X_y): """ penalty matrix must be/contain callable or auto, otherwise raise ValueError """ X, y = mcycle_X_y with pytest.raises(ValueError): gam = LinearGAM(terms=s(0, penalties='continuous')) # now do iterable with pytest.raises(ValueError): gam = LinearGAM(s(0, penalties=['continuous'])) def test_intercept(mcycle_X_y): """ should be able to just fit intercept """ X, y = mcycle_X_y gam = LinearGAM(terms=intercept) gam.fit(X, y) def test_require_one_term(mcycle_X_y): """ need at least one term """ X, y = mcycle_X_y gam = LinearGAM(terms=[]) with pytest.raises(ValueError): gam.fit(X, y) def test_linear_regression(mcycle_X_y): """ should be able to do linear regression """ X, y = mcycle_X_y gam = LinearGAM(l(0)).fit(X, y) assert(gam._is_fitted) def test_compute_stats_even_if_not_enough_iters(default_X_y): """ GAM should collect model statistics after optimization ends even if it didnt converge """ X, y = default_X_y gam = LogisticGAM(max_iter=1).fit(X, y) assert(hasattr(gam, 'statistics_')) def test_easy_plural_arguments(wage_X_y): """ it should easy to set global term arguments """ X, y = wage_X_y gam = LinearGAM(n_splines=10).fit(X, y) assert gam._is_fitted assert gam.n_splines == [10] * X.shape[1] class TestRegressions(object): def test_no_explicit_terms_custom_lambda(self, wage_X_y): X, y = wage_X_y # before easy-pluralization, this command would fail gam = LinearGAM(lam=0.6).gridsearch(X, y) assert gam._is_fitted # same with gam = LinearGAM() gam.n_splines = 10 gam.gridsearch(X, y) assert gam._is_fitted def test_n_splines_not_int(self, mcycle_X_y): """ used to fail for n_splines of type np.int64, as returned by np.arange """ X, y = mcycle_X_y gam = LinearGAM(n_splines=np.arange(9,10)[0]).fit(X, y) assert gam._is_fitted # TODO categorical dtypes get no fit linear even if fit linear TRUE # TODO categorical dtypes get their own number of splines # TODO can force continuous dtypes on categorical vars if wanted PKTSM&QZ( ( pygam/tests/test_GAMs.py# -*- coding: utf-8 -*- import pytest from pygam import * def test_can_build_sub_models(): """ check that the inits of all the sub-models are correct """ LinearGAM() LogisticGAM() PoissonGAM() GammaGAM() InvGaussGAM() ExpectileGAM() assert(True) def test_LinearGAM_uni(mcycle_X_y): """ check that we can fit a Linear GAM on real, univariate data """ X, y = mcycle_X_y gam = LinearGAM().fit(X, y) assert(gam._is_fitted) def test_LinearGAM_multi(wage_X_y): """ check that we can fit a Linear GAM on real, multivariate data """ X, y = wage_X_y gam = LinearGAM().fit(X, y) assert(gam._is_fitted) def test_LogisticGAM(default_X_y): """ check that we can fit a Logistic GAM on real data """ X, y = default_X_y gam = LogisticGAM().fit(X, y) assert(gam._is_fitted) def test_PoissonGAM(coal_X_y): """ check that we can fit a Poisson GAM on real data """ X, y = coal_X_y gam = PoissonGAM().fit(X, y) assert(gam._is_fitted) def test_InvGaussGAM(trees_X_y): """ check that we can fit a InvGauss GAM on real data """ X, y = trees_X_y gam = InvGaussGAM().fit(X, y) assert(gam._is_fitted) def test_GammaGAM(trees_X_y): """ check that we can fit a Gamma GAM on real data """ X, y = trees_X_y gam = GammaGAM().fit(X, y) assert(gam._is_fitted) def test_CustomGAM(trees_X_y): """ check that we can fit a Custom GAM on real data """ X, y = trees_X_y gam = GAM(distribution='gamma', link='inverse').fit(X, y) assert(gam._is_fitted) def test_ExpectileGAM_uni(mcycle_X_y): """ check that we can fit an Expectile GAM on real, univariate data """ X, y = mcycle_X_y gam = ExpectileGAM().fit(X, y) assert(gam._is_fitted) def test_ExpectileGAM_bad_expectiles(mcycle_X_y): """ check that get errors for unacceptable expectiles """ X, y = mcycle_X_y with pytest.raises(ValueError): ExpectileGAM(expectile=0).fit(X, y) with pytest.raises(ValueError): ExpectileGAM(expectile=1).fit(X, y) with pytest.raises(ValueError): ExpectileGAM(expectile=-0.1).fit(X, y) with pytest.raises(ValueError): ExpectileGAM(expectile=1.1).fit(X, y) # TODO check dicts: DISTRIBUTIONS etc PKIM bbpygam/tests/test_core.py# -*- coding: utf-8 -*- import numpy as np import pytest from pygam.core import * def test_Core_class(): """ test attributes of core class """ c = Core() assert(c._name == None) c = Core(name='cat', line_width=70, line_offset=3) assert(c._name == 'cat') assert(c._line_width == 70) assert(c._line_offset == 3) def test_nice_repr(): """ test a simple repr for a fake object """ param_kvs = {} out = nice_repr('hi', param_kvs, line_width=30, line_offset=5, decimals=3) assert(out == "hi()") def test_nice_repr_more_attrs(): """ test a simple repr for a fake object with more attrs """ param_kvs = {'color': 'blue', 'n_ears': 3, 'height':1.3336} out = nice_repr('hi', param_kvs, line_width=60, line_offset=5, decimals=3) assert(out == "hi(color='blue', height=1.334, n_ears=3)") PKTSM_W pygam/tests/test_datasets.py# -*- coding: utf-8 -*- import numpy as np import pytest from pygam.datasets import cake from pygam.datasets import coal from pygam.datasets import default from pygam.datasets import faithful from pygam.datasets import hepatitis from pygam.datasets import mcycle from pygam.datasets import trees from pygam.datasets import wage from pygam.datasets import chicago from pygam.datasets import toy_interaction from pygam.datasets import __all__ as DATASETS def _test_dataset(dataset_loader, n_rows, n_columns_X, n_columns_df, n_rows_X=None): """check the length of the dataset is the same regardless of the transformation check the columns of the dataset are correct in X_y and as a DataFrame check the transformation is correct check dtype is float for X_y check ndim for X is 2 Parameters ---------- dataset_loader : function, returns a dataframe or a tuple of arrays n_rows : int, expected number of rows in dataset n_columns_X : int, expected number of columns in the transformed dataset independent variables n_columns_df : int, expected number of columns in the original dataset dataframe n_rows_X : None, or int, expected number of rows in the transformed dataset independent variables if different from the original. This is usually necessary for datasets that use histogram transforms Returns ------- None """ if n_rows_X is None: n_rows_X = n_rows df = dataset_loader(return_X_y=False) X_y = dataset_loader(return_X_y=True) # number of rows never changes assert df.shape[0] == n_rows assert X_y[0].shape[0] == X_y[1].shape[0] == n_rows_X # check columns assert df.shape[1] == n_columns_df assert X_y[0].shape[1] == n_columns_X # check dtype assert X_y[0].dtype == X_y[1].dtype == 'float' # check shape assert X_y[0].ndim == 2 def test_cake(): _test_dataset(cake, n_rows=270, n_columns_X=3, n_columns_df=5) def test_coal(): _test_dataset(coal, n_rows=191, n_columns_X=1, n_columns_df=1, n_rows_X=150) def test_default(): _test_dataset(default, n_rows=10000, n_columns_X=3, n_columns_df=4) def test_faithful(): _test_dataset(faithful, n_rows=272, n_columns_X=1, n_columns_df=2, n_rows_X=200) def test_hepatitis(): _test_dataset(hepatitis, n_rows=86, n_columns_X=1, n_columns_df=3, n_rows_X=83) def test_mcycle(): _test_dataset(mcycle, n_rows=133, n_columns_X=1, n_columns_df=2) def test_trees(): _test_dataset(trees, n_rows=31, n_columns_X=2, n_columns_df=3) def test_chicago(): _test_dataset(chicago, n_rows=5114, n_columns_X=4, n_columns_df=7, n_rows_X=4863) def test_toy_interaction(): _test_dataset(toy_interaction, n_rows=50000, n_columns_X=2, n_columns_df=3) PKTSMCFpygam/tests/test_gridsearch.py# -*- coding: utf-8 -*- import numpy as np import pytest from pygam import * def test_gridsearch_returns_scores(mcycle_X_y): """ check that gridsearch returns the expected number of models """ n = 5 X, y = mcycle_X_y gam = LinearGAM() scores = gam.gridsearch(X, y, lam=np.logspace(-3,3, n), return_scores=True) assert(len(scores) == n) def test_gridsearch_returns_extra_score_if_fitted(mcycle_X_y): """ check that gridsearch returns an extra score if our model is pre-fitted """ n = 5 X, y = mcycle_X_y gam = LinearGAM().fit(X, y) scores = gam.gridsearch(X, y, lam=np.logspace(-3,3, n), return_scores=True) assert(len(scores) == n + 1) def test_gridsearch_keep_best(mcycle_X_y): """ check that gridsearch returns worse model if keep_best=False """ n = 5 X, y = mcycle_X_y gam = LinearGAM(lam=1000000).fit(X, y) score1 = gam.statistics_['GCV'] scores = gam.gridsearch(X, y, lam=np.logspace(-3,3, n), keep_best=False, return_scores=True) assert(np.min(list(scores.values())) < score1) def test_gridsearch_improves_objective(mcycle_X_y): """ check that gridsearch improves model objective """ n = 21 X, y = mcycle_X_y gam = LinearGAM().fit(X, y) objective_0 = gam.statistics_['GCV'] gam = LinearGAM().gridsearch(X, y, lam=np.logspace(-2,0, n)) objective_1 = gam.statistics_['GCV'] assert(objective_1 <= objective_0) def test_gridsearch_all_dimensions_same(cake_X_y): """ check that gridsearch searches all dimensions of lambda with equal values """ n = 5 X, y = cake_X_y scores = LinearGAM().gridsearch(X, y, lam=np.logspace(-3,3, n), return_scores=True) assert(len(scores) == n) assert(X.shape[1] > 1) def test_gridsearch_all_dimensions_independent(cake_X_y): """ check that gridsearch searches all dimensions of lambda independently """ n = 4 X, y = cake_X_y m = X.shape[1] scores = LinearGAM().gridsearch(X, y, lam=[np.logspace(-3,3, n)]*m, return_scores=True) assert(len(scores) == n**m) assert(m > 1) def test_no_cartesian_product(cake_X_y): """ check that gridsearch does not do a cartesian product when a 2D numpy array is passed as the grid and the number of columns matches the len of the parameter """ n = 5 X, y = cake_X_y m = X.shape[1] lams = np.array([np.logspace(-3,3, n)]*m).T assert lams.shape == (n, m) scores = LinearGAM().gridsearch(X, y, lam=lams, return_scores=True) assert(len(scores) == n) assert(m > 1) def test_wrong_grid_shape(cake_X_y): """ check that gridsearch raises a ValueError when the grid shape cannot be interpretted """ X, y = cake_X_y lams = np.random.rand(50, X.shape[1] + 1) with pytest.raises(ValueError): scores = LinearGAM().gridsearch(X, y, lam=lams, return_scores=True) lams = lams.T.tolist() assert len(lams) == X.shape[1] + 1 with pytest.raises(ValueError): scores = LinearGAM().gridsearch(X, y, lam=lams, return_scores=True) def test_GCV_objective_is_for_unknown_scale(mcycle_X_y, default_X_y, coal_X_y, trees_X_y): """ check that we use the GCV objective only for models with unknown scale & attempting to use it for models with known scale should return ValueError """ lam = np.linspace(1e-3, 1e3, 2) unknown_scale = [(LinearGAM, mcycle_X_y), (GammaGAM, trees_X_y), (InvGaussGAM, trees_X_y)] known_scale = [(LogisticGAM, default_X_y), (PoissonGAM, coal_X_y)] for gam, (X, y) in unknown_scale: scores1 = list(gam().gridsearch(X, y, lam=lam, objective='auto', return_scores=True).values()) scores2 = list(gam().gridsearch(X, y, lam=lam, objective='GCV', return_scores=True).values()) assert(np.allclose(scores1, scores2)) for gam, (X, y) in known_scale: try: list(gam().gridsearch(X, y, lam=lam, objective='GCV', return_scores=True).values()) except ValueError: assert(True) def test_UBRE_objective_is_for_known_scale(mcycle_X_y, default_X_y, coal_X_y, trees_X_y): """ check that we use the UBRE objective only for models with known scale & attempting to use it for models with unknown scale should return ValueError """ lam = np.linspace(1e-3, 1e3, 2) unknown_scale = [(LinearGAM, mcycle_X_y), (GammaGAM, trees_X_y), (InvGaussGAM, trees_X_y)] known_scale = [(LogisticGAM, default_X_y), (PoissonGAM, coal_X_y)] for gam, (X, y) in known_scale: scores1 = list(gam().gridsearch(X, y, lam=lam, objective='auto', return_scores=True).values()) scores2 = list(gam().gridsearch(X, y, lam=lam, objective='UBRE', return_scores=True).values()) assert(np.allclose(scores1, scores2)) for gam, (X, y) in unknown_scale: try: list(gam().gridsearch(X, y, lam=lam, objective='UBRE', return_scores=True).values()) except ValueError: assert(True) def test_no_models_fitted(mcycle_X_y): """ test no models fitted returns orginal gam """ X, y = mcycle_X_y scores = LinearGAM().gridsearch(X, y, lam=[-3, -2,-1], return_scores=True) # scores is not a dict of scores but an (unfitted) gam! assert(not isinstance(scores, dict)) assert(isinstance(scores, LinearGAM)) assert(not scores._is_fitted) PKTSMII&pygam/tests/test_partial_dependence.py# -*- coding: utf-8 -*- import sys import numpy as np import pytest import scipy as sp from pygam import * class TestPartialDepencence(object): def test_partial_dependence_on_univar_data(self, mcycle_X_y): """ partial dependence with univariate data should equal the overall model if fit intercept is false """ X, y = mcycle_X_y gam = LinearGAM(fit_intercept=False).fit(X, y) pred = gam.predict(X) pdep = gam.partial_dependence(term=0, X=X) assert((pred == pdep.ravel()).all()) def test_partial_dependence_on_univar_data2(self, mcycle_X_y, mcycle_gam): """ partial dependence with univariate data should NOT equal the overall model if fit intercept is false """ X, y = mcycle_X_y pred = mcycle_gam.predict(X) pdep = mcycle_gam.partial_dependence(term=0, X=X) assert((pred != pdep.ravel()).all()) def test_partial_dependence_feature_doesnt_exist(self, mcycle_gam): """ partial dependence should raise ValueError when requesting a nonexistent term """ with pytest.raises(ValueError): mcycle_gam.partial_dependence(term=10) def test_partial_dependence_gives_correct_shape_no_meshgrid(self, chicago_gam, chicago_X_y): """ when `meshgrid=False`, partial dependence method should return - n points if no X is supplied - same n_samples as X """ # specify X X, y = chicago_X_y for i, term in enumerate(chicago_gam.terms): if term.isintercept: continue # no confidence intervals, specify X pdep = chicago_gam.partial_dependence(term=i, X=X) assert pdep.shape == y.shape # no confidence intervals, no X pdep = chicago_gam.partial_dependence(term=i) assert pdep.shape == (100**len(term),) # with confidence intervals, specify X pdep, confi = chicago_gam.partial_dependence(term=i, X=X, width=0.95) assert pdep.shape == y.shape assert confi.shape == (y.shape[0], 2) # with confidence intervals, no X pdep, confi = chicago_gam.partial_dependence(term=i, width=0.95) assert pdep.shape == (100**len(term),) assert confi.shape == (100**len(term), 2) def test_partial_dependence_gives_correct_shape_with_meshgrid(self, chicago_gam, chicago_X_y): """ when `meshgrid=True`, partial dependence method should return - pdep is meshes with the dimension of the term - confi is meshes with the dimension of the term, and number of confis """ # specify X X, y = chicago_X_y for i, term in enumerate(chicago_gam.terms): if term.isintercept: continue # easy way to make a meshgrid to input XX = chicago_gam.generate_X_grid(term=i, meshgrid=True, n=50) # no confidence intervals, specify X pdep = chicago_gam.partial_dependence(term=i, X=XX, meshgrid=True) assert pdep.shape == (50,) * len(term) # no confidence intervals, no X pdep = chicago_gam.partial_dependence(term=i, meshgrid=True) assert pdep.shape == (100,) * len(term) # with confidence intervals, specify X pdep, confi = chicago_gam.partial_dependence(term=i, X=XX, meshgrid=True, width=0.95) assert pdep.shape == (50,) * len(term) assert confi.shape == (50,) * len(term) + (2,) # with confidence intervals, no X pdep, confi = chicago_gam.partial_dependence(term=i, meshgrid=True, width=0.95) assert pdep.shape == (100,) * len(term) assert confi.shape == (100,) * len(term) +(2,) def test_partital_dependence_width_and_quantiles_equivalent(self, chicago_gam, chicago_X_y): """ for non-tensor terms, the outputs of `partial_dependence` is the same regardless of `meshgrid=True/False` """ assert not chicago_gam.terms[0].istensor meshTrue = chicago_gam.partial_dependence(term=0, meshgrid=True) meshFalse = chicago_gam.partial_dependence(term=0, meshgrid=False) assert (meshTrue == meshFalse).all() def test_partial_dependence_meshgrid_true_false_equivalent_for_non_tensors(self, chicago_gam, chicago_X_y): """ for tensor terms the value of `meshgrid` matters """ assert chicago_gam.terms[1].istensor meshTrue = chicago_gam.partial_dependence(term=1, meshgrid=True) meshFalse = chicago_gam.partial_dependence(term=1, meshgrid=False) assert meshTrue.shape != meshFalse.shape assert meshTrue.size == meshFalse.size def test_intercept_raises_error_for_partial_dependence(self, mcycle_X_y): """ if a user asks for the intercept when none is fitted, a ValueError is raised """ X, y = mcycle_X_y gam_intercept = LinearGAM(fit_intercept=True).fit(X, y) with pytest.raises(ValueError): pdeps = gam_intercept.partial_dependence(term=-1) gam_no_intercept = LinearGAM(fit_intercept=False).fit(X, y) pdeps = gam_no_intercept.partial_dependence(term=-1) def test_no_X_needed_for_partial_dependence(self, mcycle_gam): """ partial_dependence() method uses generate_X_grid by default for the X array """ XX = mcycle_gam.generate_X_grid(term=0) assert (mcycle_gam.partial_dependence(term=0) == mcycle_gam.partial_dependence(term=0, X=XX)).all() PKTSM$rH H pygam/tests/test_penalties.py# -*- coding: utf-8 -*- import numpy as np import pytest from pygam import * from pygam.penalties import derivative from pygam.penalties import l2 from pygam.penalties import monotonic_inc from pygam.penalties import monotonic_dec from pygam.penalties import convex from pygam.penalties import concave from pygam.penalties import none from pygam.penalties import wrap_penalty def test_single_spline_penalty(): """ check that feature functions with only 1 basis are penalized correctly derivative penalty should be 0. l2 should penalty be 1. monotonic_ and convexity_ should be 0. """ coef = np.array(1.) assert(np.alltrue(derivative(1, coef).A == 0.)) assert(np.alltrue(l2(1, coef).A == 1.)) assert(np.alltrue(monotonic_inc(1, coef).A == 0.)) assert(np.alltrue(monotonic_dec(1, coef).A == 0.)) assert(np.alltrue(convex(1, coef).A == 0.)) assert(np.alltrue(concave(1, coef).A == 0.)) assert(np.alltrue(none(1, coef).A == 0.)) def test_wrap_penalty(): """ check that wrap penalty indeed reduces inserts the desired penalty into the linear term when fit_linear is True, and 0, when fit_linear is False. """ coef = np.array(1.) n = 2 linear_penalty = -1 fit_linear = True p = wrap_penalty(none, fit_linear, linear_penalty=linear_penalty) P = p(n, coef).A assert(P.sum() == linear_penalty) fit_linear = False p = wrap_penalty(none, fit_linear, linear_penalty=linear_penalty) P = p(n, coef).A assert(P.sum() == 0.) def test_monotonic_inchepatitis_X_y(hepatitis_X_y): """ check that monotonic_inc constraint produces monotonic increasing function """ X, y = hepatitis_X_y gam = LinearGAM(terms=s(0, constraints='monotonic_inc')) gam.fit(X, y) XX = gam.generate_X_grid(term=0) Y = gam.predict(np.sort(XX)) diffs = np.diff(Y, n=1) assert(((diffs >= 0) + np.isclose(diffs, 0.)).all()) def test_monotonic_dec(hepatitis_X_y): """ check that monotonic_dec constraint produces monotonic decreasing function """ X, y = hepatitis_X_y gam = LinearGAM(terms=s(0, constraints='monotonic_dec')) gam.fit(X, y) XX = gam.generate_X_grid(term=0) Y = gam.predict(np.sort(XX)) diffs = np.diff(Y, n=1) assert(((diffs <= 0) + np.isclose(diffs, 0.)).all()) def test_convex(hepatitis_X_y): """ check that convex constraint produces convex function """ X, y = hepatitis_X_y gam = LinearGAM(terms=s(0, constraints='convex')) gam.fit(X, y) XX = gam.generate_X_grid(term=0) Y = gam.predict(np.sort(XX)) diffs = np.diff(Y, n=2) assert(((diffs >= 0) + np.isclose(diffs, 0.)).all()) def test_concave(hepatitis_X_y): """ check that concave constraint produces concave function """ X, y = hepatitis_X_y gam = LinearGAM(terms=s(0, constraints='concave')) gam.fit(X, y) XX = gam.generate_X_grid(term=0) Y = gam.predict(np.sort(XX)) diffs = np.diff(Y, n=2) assert(((diffs <= 0) + np.isclose(diffs, 0.)).all()) # TODO penalties gives expected matrix structure # TODO circular constraints PK_M7 K/K/pygam/tests/test_terms.py# -*- coding: utf-8 -*- from copy import deepcopy import numpy as np import pytest from pygam import * from pygam.terms import Term, Intercept, SplineTerm, LinearTerm, FactorTerm, TensorTerm, TermList from pygam.utils import flatten @pytest.fixture def chicago_gam(chicago_X_y): X, y = chicago_X_y gam = PoissonGAM(terms=s(0, n_splines=200) + te(3, 1) + s(2)).fit(X, y) return gam def test_wrong_length(): """iterable params must all match lengths """ with pytest.raises(ValueError): SplineTerm(0, lam=[0, 1, 2], penalties=['auto', 'auto']) def test_num_coefs(mcycle_X_y, wage_X_y): """make sure this method gives correct values """ X, y = mcycle_X_y term = Intercept().compile(X) assert term.n_coefs == 1 term = LinearTerm(0).compile(X) assert term.n_coefs == 1 term = SplineTerm(0).compile(X) assert term.n_coefs == term.n_splines X, y = wage_X_y term = FactorTerm(2).compile(X) assert term.n_coefs == 5 term_a = SplineTerm(0).compile(X) term_b = SplineTerm(1).compile(X) term = TensorTerm(term_a, term_b).compile(X) assert term.n_coefs == term_a.n_coefs * term_b.n_coefs def test_term_list_removes_duplicates(): """prove that we remove duplicated terms""" term = SplineTerm(0) term_list = term + term assert isinstance(term_list, TermList) assert len(term_list) == 1 def test_tensor_invariance_to_scaling(chicago_gam, chicago_X_y): """a model with tensor terms should give results regardless of input scaling """ X, y = chicago_X_y X[:, 3] = X[:, 3] * 100 gam = PoissonGAM(terms=s(0, n_splines=200) + te(3, 1) + s(2)).fit(X, y) assert np.allclose(gam.coef_, chicago_gam.coef_, atol=1e-6) def test_tensor_must_have_at_least_2_marginal_terms(): with pytest.raises(ValueError): te(0) def test_tensor_term_expands_args_to_match_penalties_and_terms(): tensor = te(0, 1, lam=3) assert len(tensor.lam) == 2 assert len(flatten(tensor.lam)) == 2 tensor = te(0, 1, penalties='auto') assert len(tensor.lam) == 2 assert len(flatten(tensor.lam)) == 2 tensor = te(0, 1, penalties=['auto', ['auto', 'auto']]) assert len(tensor.lam) == 2 assert len(flatten(tensor.lam)) == 3 def test_tensor_term_skips_kwargs_when_marginal_term_is_supplied(): tensor = te(0, s(1), n_splines=420) assert tensor._terms[0].n_coefs == 420 assert tensor._terms[1].n_coefs != 420 def test_tensor_term_doesnt_accept_tensor_terms(): with pytest.raises(ValueError): te(l(0), te(0, 1)) def test_tensor_args_length_must_agree_with_number_of_terms(): with pytest.raises(ValueError): te(0, 1, lam=[3]) with pytest.raises(ValueError): te(0, 1, lam=[3]) with pytest.raises(ValueError): te(0, 1, lam=[3, 3, 3]) def test_build_from_info(): """we can rebuild terms from info """ terms = [Intercept(), LinearTerm(0), SplineTerm(0), FactorTerm(0), TensorTerm(0,1)] for term in terms: assert Term.build_from_info(term.info) == term assert te(0, 1) == TensorTerm(SplineTerm(0, n_splines=10), SplineTerm(1, n_splines=10)) def test_by_variable(): """our fit on the toy tensor dataset with a by variable on the linear feature should be similar to the fit with a tensor product of a spline with a linear term """ pass def test_by_variable_doesnt_exist_in_X(mcycle_X_y): """raises a value error if we cannot locate the by variable """ term = s(0, by=1) with pytest.raises(ValueError): term.compile(mcycle_X_y[0]) def test_term_list_from_info(): """we can remake a term list from info """ term_list = SplineTerm(0) + LinearTerm(1) assert Term.build_from_info(term_list.info) == term_list def test_term_list_only_accepts_terms_or_term_list(): TermList() with pytest.raises(ValueError): TermList(None) def test_pop_term_from_term_list(): term_list = SplineTerm(0) + LinearTerm(1) + Intercept() term_list_2 = deepcopy(term_list) # by default we pop the last assert term_list_2.pop() == term_list[-1] assert term_list_2.pop(0) == term_list[0] with pytest.raises(ValueError): term_list_2.pop(1) == term_list[0] def test_no_multiply(): """trying to multiply terms raises an error """ with pytest.raises(NotImplementedError): SplineTerm(0) * LinearTerm(1) term_list = SplineTerm(0) + LinearTerm(1) with pytest.raises(NotImplementedError): term_list * term_list def test_by_is_similar_to_tensor_with_linear_term(toy_interaction_X_y): """for simple interactions we can acheive equivalent fits using: - a spline with a by-variable - a tensor between spline and a linear term """ X, y = toy_interaction_X_y gam_a = LinearGAM(te(s(0, n_splines=20), l(1))).fit(X, y) gam_b = LinearGAM(s(0, by=1)).fit(X, y) r2_a = gam_a.statistics_['pseudo_r2']['explained_deviance'] r2_b = gam_b.statistics_['pseudo_r2']['explained_deviance'] assert np.allclose(r2_a, r2_b) def test_correct_smoothing_in_tensors(toy_interaction_X_y): """check that smoothing penalties are correctly computed across the marginal dimensions feature 0 is the sinusoid, so this one needs to be wiggly feature 1 is the linear function, so this can smoothed heavily """ X, y = toy_interaction_X_y # increase smoothing on linear function heavily, to no detriment gam = LinearGAM(te(0, 1, lam=[0.6, 10000])).fit(X, y) assert gam.statistics_['pseudo_r2']['explained_deviance'] > 0.9 # smoothing the sinusoid function heavily reduces fit quality gam = LinearGAM(te(0, 1, lam=[10000, 0.6])).fit(X, y) assert gam.statistics_['pseudo_r2']['explained_deviance'] < 0.1 def test_dummy_encoding(wage_X_y, wage_gam): """check that dummy encoding produces fewer coefficients than one-hot""" X, y = wage_X_y gam = LinearGAM(s(0) + s(1) + f(2, coding='dummy')).fit(X, y) assert gam._modelmat(X=X, term=2).shape[1] == 4 assert gam.terms[2].n_coefs == 4 assert wage_gam._modelmat(X=X, term=2).shape[1] == 5 assert wage_gam.terms[2].n_coefs == 5 def test_build_cyclic_p_spline(hepatitis_X_y): """check the cyclic p spline builds the r2 for a cyclic gam on a obviously aperiodic function should suffer """ X, y = hepatitis_X_y # unconstrained gam gam = LinearGAM(s(0)).fit(X, y) r_unconstrained = gam.statistics_['pseudo_r2']['explained_deviance'] # cyclic gam gam = LinearGAM(s(0, basis='cp')).fit(X, y) r_cyclic = gam.statistics_['pseudo_r2']['explained_deviance'] assert r_unconstrained > r_cyclic def test_cyclic_p_spline_periodicity(hepatitis_X_y): """check the cyclic p spline behavioves periodically namely: - the value at the edge knots should be the same - extrapolation should be periodic """ X, y = hepatitis_X_y gam = LinearGAM(s(0, basis='cp')).fit(X, y) # check periodicity left = gam.edge_knots_[0][1] right = gam.edge_knots_[0][1] assert(gam.predict(left) == gam.predict(right)) # check extrapolation further = right + (right - left) assert(gam.predict(further) == gam.predict(right)) def test_cyclic_p_spline_custom_period(): """show that we can set custom edge_knots, and that these affect our model's performance """ # define square wave X = np.linspace(0, 1, 5000) y = X > 0.5 # when modeling the full period, we get close with a periodic basis gam = LinearGAM(s(0, basis='cp', n_splines=4, spline_order=0)).fit(X, y) assert np.allclose(gam.predict(X), y) assert np.allclose(gam.edge_knots_[0], [0, 1]) # when modeling a non-periodic function, our periodic model fails gam = LinearGAM(s(0, basis='cp', n_splines=4, spline_order=0, edge_knots=[0, 0.5])).fit(X, y) assert np.allclose(gam.predict(X), 0.5) assert np.allclose(gam.edge_knots_[0], [0, 0.5]) def test_tensor_terms_have_constraints(toy_interaction_X_y): """test that we can fit a gam with constrained tensor terms, even if those constraints are 'none' """ X, y = toy_interaction_X_y gam = LinearGAM(te(0, 1, constraints='none')).fit(X, y) assert gam._is_fitted assert gam.terms.hasconstraint def test_tensor_composite_constraints_equal_penalties(): """check that the composite constraint matrix for a tensor term is equivalent to a penalty matrix under the correct conditions """ from pygam.penalties import derivative def der1(*args, **kwargs): kwargs.update({'derivative':1}) return derivative(*args, **kwargs) # create a 3D tensor where the penalty should be equal to the constraint term = te(0, 1, 2, n_splines=[4, 5, 6], penalties=der1, lam=1, constraints='monotonic_inc') # check all the dimensions for i in range(3): P = term._build_marginal_penalties(i).A C = term._build_marginal_constraints(i, -np.arange(term.n_coefs), constraint_lam=1, constraint_l2=0).A assert (P == C).all() def test_tensor_with_constraints(hepatitis_X_y): """we should be able to fit a gam with not 'none' constraints on a tensor term and observe its effect in reducing the R2 of the fit """ X, y = hepatitis_X_y X = np.c_[X, np.random.randn(len(X))] # add a random interaction data # constrain useless dimension gam_useless_constraint = LinearGAM(te(0, 1, constraints=['none', 'monotonic_dec'], n_splines=[20, 4])) gam_useless_constraint.fit(X, y) # constrain informative dimension gam_constrained = LinearGAM(te(0, 1, constraints=['monotonic_dec', 'none'], n_splines=[20, 4])) gam_constrained.fit(X, y) assert gam_useless_constraint.statistics_['pseudo_r2']['explained_deviance'] > 0.5 assert gam_constrained.statistics_['pseudo_r2']['explained_deviance'] < 0.1 class TestRegressions(object): def test_no_auto_dtype(self): with pytest.raises(ValueError): SplineTerm(feature=0, dtype='auto') def test_compose_penalties(self): """penalties should be composable, and this is done by adding all penalties on a single term, NOT multiplying them. so a term with a derivative penalty and a None penalty should be equvalent to a term with a derivative penalty. """ base_term = SplineTerm(0) term = SplineTerm(feature=0, penalties=['auto', 'none']) # penalties should be equivalent assert (term.build_penalties() == base_term.build_penalties()).A.all() # multitple penalties should be additive, not multiplicative, # so 'none' penalty should have no effect assert np.abs(term.build_penalties().A).sum() > 0 def test_compose_constraints(self, hepatitis_X_y): """we should be able to compose penalties here we show that a gam with a monotonic increasing penalty composed with a monotonic decreasing penalty is equivalent to a gam with only an intercept """ X, y = hepatitis_X_y gam_compose = LinearGAM(s(0, constraints=['monotonic_inc', 'monotonic_dec'])).fit(X, y) gam_intercept = LinearGAM(terms=None).fit(X, y) assert np.allclose(gam_compose.coef_[-1], gam_intercept.coef_) def test_constraints_and_tensor(self, chicago_X_y): """a model that has consrtraints and tensor terms should not fail to build because of inability of tensor terms to build a 'none' constraint """ X, y = chicago_X_y gam = PoissonGAM(s(0, constraints='monotonic_inc') + te(3, 1) + s(2)).fit(X, y) assert gam._is_fitted PKTSM,,pygam/tests/test_utils.py# -*- coding: utf-8 -*- from copy import deepcopy try: # py >= 3.3 from unittest.mock import patch except ImportError: # py < 3.3 from mock import patch import numpy as np import pytest from pygam import * from pygam.utils import check_X, check_y, check_X_y, sig_code, check_iterable_depth # TODO check dtypes works as expected # TODO checkX, checky, check XY expand as needed, call out bad domain @pytest.fixture def wage_gam(wage_X_y): X, y = wage_X_y gam = LinearGAM(s(0) + s(1) + f(2)).fit(X,y) return gam @pytest.fixture def default_gam(default_X_y): X, y = default_X_y gam = LogisticGAM().fit(X,y) return gam def test_check_X_categorical_prediction_exceeds_training(wage_X_y, wage_gam): """ if our categorical variable is outside the training range we should get an error """ X, y = wage_X_y # last feature is categorical gam = wage_gam # get edge knots for last feature eks = gam.edge_knots_[-1] # add 1 to all Xs, thus pushing some X past the max value X[:,-1] = eks[-1] + 1 with pytest.raises(ValueError): gam.predict(X) def test_check_y_not_int_not_float(wage_X_y, wage_gam): """y must be int or float, or we should get a value error""" X, y = wage_X_y y_str = ['hi'] * len(y) with pytest.raises(ValueError): check_y(y_str, wage_gam.link, wage_gam.distribution) def test_check_y_casts_to_numerical(wage_X_y, wage_gam): """check_y will try to cast data to numerical types""" X, y = wage_X_y y = y.astype('object') y = check_y(y, wage_gam.link, wage_gam.distribution) assert y.dtype == 'float' def test_check_y_not_min_samples(wage_X_y, wage_gam): """check_y expects a minimum number of samples""" X, y = wage_X_y with pytest.raises(ValueError): check_y(y, wage_gam.link, wage_gam.distribution, min_samples=len(y)+1, verbose=False) def test_check_y_not_in_domain_link(default_X_y, default_gam): """if you give labels outide of the links domain, check_y will raise an error""" X, y = default_X_y gam = default_gam with pytest.raises(ValueError): check_y(y + .1, default_gam.link, default_gam.distribution, verbose=False) def test_check_X_not_int_not_float(): """X must be an in or a float""" with pytest.raises(ValueError): check_X(['hi'], verbose=False) def test_check_X_too_many_dims(): """check_X accepts at most 2D inputs""" with pytest.raises(ValueError): check_X(np.ones((5,4,3))) def test_check_X_not_min_samples(): with pytest.raises(ValueError): check_X(np.ones((5)), min_samples=6, verbose=False) def test_check_X_y_different_lengths(): with pytest.raises(ValueError): check_X_y(np.ones(5), np.ones(4)) def test_input_data_after_fitting(mcycle_X_y): """ our check_X and check_y functions should be invoked any time external data is input to the model """ X, y = mcycle_X_y weights = np.ones_like(y) X_nan = deepcopy(X) X_nan[0] = X_nan[0] * np.nan y_nan = deepcopy(y.values) y_nan[0] = y_nan[0] * np.nan weights_nan = deepcopy(weights) weights_nan[0] = weights_nan[0] * np.nan gam = LinearGAM() with pytest.raises(ValueError): gam.fit(X_nan, y, weights) with pytest.raises(ValueError): gam.fit(X, y_nan, weights) with pytest.raises(ValueError): gam.fit(X, y, weights_nan) gam = gam.fit(X, y) # test X is nan with pytest.raises(ValueError): gam.predict(X_nan) with pytest.raises(ValueError): gam.predict_mu(X_nan) with pytest.raises(ValueError): gam.confidence_intervals(X_nan) with pytest.raises(ValueError): gam.prediction_intervals(X_nan) with pytest.raises(ValueError): gam.partial_dependence(X_nan) with pytest.raises(ValueError): gam.deviance_residuals(X_nan, y, weights) with pytest.raises(ValueError): gam.loglikelihood(X_nan, y, weights) with pytest.raises(ValueError): gam.gridsearch(X_nan, y, weights) with pytest.raises(ValueError): gam.sample(X_nan, y) # test y is nan with pytest.raises(ValueError): gam.deviance_residuals(X, y_nan, weights) with pytest.raises(ValueError): gam.loglikelihood(X, y_nan, weights) with pytest.raises(ValueError): gam.gridsearch(X, y_nan, weights) with pytest.raises(ValueError): gam.sample(X, y_nan, weights=weights, n_bootstraps=2) # test weights is nan with pytest.raises(ValueError): gam.deviance_residuals(X, y, weights_nan) with pytest.raises(ValueError): gam.loglikelihood(X, y, weights_nan) with pytest.raises(ValueError): gam.gridsearch(X, y, weights_nan) with pytest.raises(ValueError): gam.sample(X, y, weights=weights_nan, n_bootstraps=2) def test_catch_chol_pos_def_error(default_X_y): """ regresion test doing a gridsearch with a poorly conditioned penalty matrix should not crash """ X, y = default_X_y gam = LogisticGAM().gridsearch(X, y, lam=np.logspace(10, 12, 3)) def test_pvalue_sig_codes(): """make sure we get the codes we exepct""" with pytest.raises(AssertionError): sig_code(-1) assert sig_code(0) == '***' assert sig_code(0.00101) == '**' assert sig_code(0.0101) == '*' assert sig_code(0.0501) == '.' assert sig_code(0.101) == ' ' def test_b_spline_basis_extrapolates(mcycle_X_y): X, y = mcycle_X_y gam = LinearGAM().fit(X, y) slopes = [] X = gam.generate_X_grid(term=0, n=50000) y = gam.predict(X) slopes.append((y[1] - y[0]) / (X[1] - X[0])) mean = X.mean() X -= mean X *= 1.1 X += mean y = gam.predict(X) slopes.append((y[1] - y[0]) / (X[1] - X[0])) assert np.allclose(slopes[0], slopes[1], atol=1e-4) def test_iterable_depth(): it = [[[3]]] assert check_iterable_depth(it) == 3 assert check_iterable_depth(it, max_depth=2) == 2 def test_no_SKSPIMPORT(mcycle_X_y): """make sure our module work with and without scikit-sparse """ from pygam.utils import SKSPIMPORT if SKSPIMPORT: with patch('pygam.utils.SKSPIMPORT', new=False) as SKSPIMPORT_patch: from pygam.utils import SKSPIMPORT assert SKSPIMPORT == False X, y = mcycle_X_y assert LinearGAM().fit(X, y)._is_fitted PKIMFLEEpygam-0.8.0.dist-info/LICENSE GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 Copyright (C) 2007 Free Software Foundation, Inc. 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You may not convey a covered work if you are a party to an arrangement with a third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007. Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law. 12. No Surrender of Others' Freedom. If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program. 13. Use with the GNU Affero General Public License. Notwithstanding any other provision of this License, you have permission to link or combine any covered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. 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IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. 17. Interpretation of Sections 15 and 16. If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee. END OF TERMS AND CONDITIONS How to Apply These Terms to Your New Programs If you develop a new program, and you want it to be of the greatest possible use to the public, the best way to achieve this is to make it free software which everyone can redistribute and change under these terms. To do so, attach the following notices to the program. It is safest to attach them to the start of each source file to most effectively state the exclusion of warranty; and each file should have at least the "copyright" line and a pointer to where the full notice is found. {one line to give the program's name and a brief idea of what it does.} Copyright (C) {year} {name of author} This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see . Also add information on how to contact you by electronic and paper mail. If the program does terminal interaction, make it output a short notice like this when it starts in an interactive mode: {project} Copyright (C) {year} {fullname} This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, your program's commands might be different; for a GUI interface, you would use an "about box". You should also get your employer (if you work as a programmer) or school, if any, to sign a "copyright disclaimer" for the program, if necessary. For more information on this, and how to apply and follow the GNU GPL, see . The GNU General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Lesser General Public License instead of this License. But first, please read . 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