{
    "info": {
        "author": "Danyang Su",
        "author_email": "fnosdy@gmail.com",
        "bugtrack_url": null,
        "classifiers": [
            "Development Status :: 3 - Alpha",
            "Intended Audience :: Science/Research",
            "License :: OSI Approved :: BSD License",
            "Operating System :: OS Independent",
            "Programming Language :: Python :: 3",
            "Topic :: Scientific/Engineering :: Artificial Intelligence"
        ],
        "description": "# linkalman\n\n`linkalman` is a python package that solves linear structural time series models with Gaussian noises. Compared with some other popular Kalman filter packages written in python, linkalman has a combination of several advantages:\n\n  - Account for partially and fully incomplete measurements \n  - Flexible and convenient model structure\n  - Robust and efficient implementation\n  - Proper implementation for unknown priors\n  - Built-in numerical and EM algorithm\n  - Open-source with a comprehensive user manual \n  - Modular design with intuitive model specification\n\n### Installation\n`linkalman` requires the following packages to run:\n\n  - numpy\n  - pandas\n  - networkx\n  - scipy\n \nTo install `linkalman`, simply use the standard `pip` command:\n\n```sh\n$ pip install linkalman\n```\n### Example\nHere I will provide a simple example using `linkalman`. See [here](https://github.com/DanyangSu/linkalman/tree/master/examples/jupyter_notebooks) for more examples, and [user's manual](https://github.com/DanyangSu/linkalman/blob/master/doc/manual.pdf) for technical details.\n\n```python\nimport pandas as pd\nimport numpy as np\nfrom scipy.optimize import minimize\nfrom linkalman.models import BaseConstantModel as BCM\nimport matplotlib.pyplot as plt\n\n\n# Get data\ndf = pd.read_csv('https://raw.githubusercontent.com/jbrownlee/Datasets/master/daily-total-female-births.csv')\ndf['x'] = 1\ndf.set_index('Date', inplace=True)\n```\n\nFirst we define the system dynamics of a Bayesian Structural Time Series (BSTS) model. Here I define a Stochastic linear trend model to extract the trend information from the time series (referring to the example section of [user's manual](https://github.com/DanyangSu/linkalman/blob/master/doc/manual.pdf) for details)\n```python\ndef my_f(theta):\n    sig1 = np.exp(theta[0])\n    sig2 = np.exp(theta[1])\n    sig3 = np.exp(theta[2])\n\n    F = np.array([[1, 1], [0, 1]])\n    Q = np.array([[sig1, 0], [0, sig2]]) \n    R = np.array([[sig3]])\n    H = np.array([[1, 0]])\n    # Collect system matrices\n    M = {'F': F, 'Q': Q, 'H': H, 'R': R}\n\n    return M \n```\nNext we define a solver or optimizer, you can choose any solver you prefer. Here I just use `scipy.optimize.minimize`.\n```python\ndef my_solver(param, obj_func, verbose=False, **kwargs):\n    obj_ = lambda x: -obj_func(x)\n    res = minimize(obj_, param, **kwargs)\n    theta_opt = np.array(res.x)\n    fval_opt = res.fun\n    return theta_opt, fval_opt\n```\nNow we can fit the data. First we initialize the model and feed the system dynamics (`my_f`) and solver (`my_solver`). You may also pass the keyworded arguments to for `my_f` and `my_solver`.\n```python\nmodel = BCM()\nmodel.set_f(my_f)\nmodel.set_solver(my_solver, method='nelder-mead', \n        options={'xatol': 1e-8, 'disp': True, 'maxiter': 10000})\ntheta_init = np.random.rand(3)\nmodel.fit(df, theta_init, y_col=['Births'], x_col=['x'], \n              method='LLY')\ndf_LLY = model.predict(df)\n```\nThat is it! If you want to do additional work, you can do the following to plot a confidence interval around your predictions.\n```python\ndf_LLY['kf_ub'] = df_LLY.Births_filtered + 1.96 * np.sqrt(df_LLY.Births_fvar)\ndf_LLY['kf_lb'] = df_LLY.Births_filtered - 1.96 * np.sqrt(df_LLY.Births_fvar)\ndf_LLY = df_LLY[df_LLY.index > '1959-01-01']\ndf_LLY.index = pd.to_datetime(df_LLY.index)\n\n# Define plot function\ndef simple_plot(df, col_est, col_actual, col_ub, col_lb, label_est,\n                label_actual, title, figsize=(12, 8)):\n    ax = plt.figure(figsize=figsize)\n    plt.plot(df.index, df[col_est], 'r', label=label_est)\n    plt.scatter(df_LLY.index, df[col_actual], s=20, c='b', \n                marker='o', label=label_actual)\n    plt.fill_between(df.index, df[col_ub], df[col_lb], color='g', alpha=0.2)\n    ax.legend(loc='right', fontsize=9)\n    plt.title(title, fontsize=22)\n    plt.show()\nsimple_plot(df_LLY, 'Births_filtered', 'Births', 'kf_ub', 'kf_lb',  \n           'Prediction', 'Births', 'Filtered Births Data')\n```\n\n### License\n\n3-Clause BSD",
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