{ "info": { "author": "Simone Marsili", "author_email": "simo.marsili@gmail.com", "bugtrack_url": null, "classifiers": [ "Development Status :: 3 - Alpha", "Intended Audience :: Science/Research", "License :: OSI Approved :: BSD License", "Programming Language :: Python :: 3", "Programming Language :: Python :: 3.4", "Programming Language :: Python :: 3.5", "Programming Language :: Python :: 3.6", "Topic :: Scientific/Engineering", "Topic :: Scientific/Engineering :: Artificial Intelligence", "Topic :: Scientific/Engineering :: Bio-Informatics", "Topic :: Scientific/Engineering :: Information Analysis" ], "description": "====================================================\nndd - Bayesian entropy estimation from discrete data\n====================================================\n.. image:: https://badge.fury.io/py/ndd.svg\n :target: https://badge.fury.io/py/ndd\n.. image:: https://travis-ci.com/simomarsili/ndd.svg?branch=master\n :target: https://travis-ci.com/simomarsili/ndd\n\nThe **ndd** package provides a simple Python interface to an efficient\nimplementation of the `Nemenman-Schafee-Bialek (NSB) algorithm\n`_,\na parameter-free, Bayesian entropy estimator for discrete data.\nThe NSB algorithm allows entropy estimation when the number of samples is much\nsmaller than the number of classes with non-zero probability.\n\n\nBasic usage\n===========\n\nThe **entropy** function takes as input a vector of **frequency counts**\n(the observed frequencies for a set of classes or states) and an **alphabet size**\n(the number of classes with non-zero probability, including unobserved classes)\nand returns an entropy estimate (in nats)::\n\n >>> import ndd\n >>> counts = [12, 4, 12, 4, 5, 3, 1, 5, 1, 2, 2, 2, 2, 11, 3, 4, 12, 12, 1, 2]\n >>> entropy_estimate = ndd.entropy(counts, k=100)\n >>> entropy_estimate\n 2.8246841846955486\n\nWhere to get it\n===============\nInstall using pip::\n\n pip3 install -U ndd\n\nor directly from sources in github for the latest version of the code::\n\n pip3 install git+https://github.com/simomarsili/ndd.git\n\nIn order to compile **ndd**, you will need **numpy** (>= 1.9) and a\n**Fortran compiler** installed on your machine.\nIf you are using Debian or a Debian derivative such as Ubuntu,\nyou can install the gfortran compiler using the following command::\n\n sudo apt-get install gfortran\n\nOn Windows, you can use the gfortran compiler from the\n`MinGW-w64 `_ project\n(`direct link `_\nto the installer).\n\nIf you don't have a Fortran compiler, install using the\n`ndd python wheels `_\nwith pre-compiled extensions. numpy >= 1.16 is needed.\n\nChanges\n=======\n\n**v1.6.1**\n Changed:\n Fixed numerical integration for large alphabet sizes.\n\n**v1.6**\n Changed:\n\n The signature of the *entropy* function has been changed to allow\n arbitrary entropy estimators. The new signature is::\n\n entropy(pk, k=None, estimator='NSB', return_std=False)\n\n The available estimators are::\n\n >>> import ndd\n >>> ndd.entropy_estimators\n ['Plugin', 'MillerMadow', 'NSB', 'AsymptoticNSB', 'Grassberger']\n\n Check the function docstring for details.\n\n Added:\n\n - *MillerMadow* estimator class\n - *AsymptoticNSB* estimator class\n - *Grassberger* estimator class\n\n**v1.5**\n For methods/functions working on data matrices:\n the default input is a **n-by-p** 2D array (n samples from p discrete\n variables, with different samples on different **rows**).\n Since release 1.3, the default was a transposed (**p-by-n**) data matrix.\n The behavior of functions taking frequency counts as input\n (e.g. the *entropy* function) is unchanged.\n**v1.4**\n Added the *kullback_leibler_divergence* function.\n**v1.1**\n Added:\n\n * *from_data*\n * *mutual_information*\n * *conditional_information*\n * *interaction_information*\n * *coinformation*\n**v1.0**\n Drop support for Python < 3.4.\n**v0.9**\n Added the `jensen_shannnon_divergence` function.\n\nReferences\n==========\n\nSome refs::\n\n @article{wolpert1995estimating,\n title={Estimating functions of probability distributions from a finite set of samples},\n author={Wolpert, David H and Wolf, David R},\n journal={Physical Review E},\n volume={52},\n number={6},\n pages={6841},\n year={1995},\n publisher={APS}\n }\n\n @inproceedings{nemenman2002entropy,\n title={Entropy and inference, revisited},\n author={Nemenman, Ilya and Shafee, Fariel and Bialek, William},\n booktitle={Advances in neural information processing systems},\n pages={471--478},\n year={2002}\n }\n\n @article{paninski2003estimation,\n title={Estimation of entropy and mutual information},\n author={Paninski, Liam},\n journal={Neural computation},\n volume={15},\n number={6},\n pages={1191--1253},\n year={2003},\n publisher={MIT Press}\n }\n\n @article{nemenman2004entropy,\n title={Entropy and information in neural spike trains: Progress on the sampling problem},\n author={Nemenman, Ilya and Bialek, William and van Steveninck, Rob de Ruyter},\n journal={Physical Review E},\n volume={69},\n number={5},\n pages={056111},\n year={2004},\n publisher={APS}\n }\n\n @article{nemenman2011coincidences,\n title={Coincidences and estimation of entropies of random variables with large cardinalities},\n author={Nemenman, Ilya},\n journal={Entropy},\n volume={13},\n number={12},\n pages={2013--2023},\n year={2011},\n publisher={Molecular Diversity Preservation International}\n }\n\n @article{archer2013bayesian,\n title={Bayesian and quasi-Bayesian estimators for mutual information from discrete data},\n author={Archer, Evan and Park, Il Memming and Pillow, Jonathan W},\n journal={Entropy},\n volume={15},\n number={5},\n pages={1738--1755},\n year={2013},\n publisher={Multidisciplinary Digital Publishing Institute}\n }\n\n @article{archer2014bayesian,\n title={Bayesian entropy estimation for countable discrete distributions},\n author={Archer, Evan and Park, Il Memming and Pillow, Jonathan W},\n journal={The Journal of Machine Learning Research},\n volume={15},\n number={1},\n pages={2833--2868},\n year={2014},\n publisher={JMLR. org}\n }\n\n\nand interesting links:\n\n- `Sebastian Nowozin on Bayesian estimators `_\n\n- `Il Memming Park on discrete entropy estimators `_\n\nContributing\n============\n\n**ndd** is an OPEN Source Project so please help out by `reporting bugs `_ or forking and opening pull requests when possible.\n\nLicense\n=======\n\nCopyright (c) 2016-2019, Simone Marsili.\nAll rights reserved.\n\nRedistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:\n\n1. 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