ndd 1.4.1

Bayesian entropy estimation from discrete data

The ndd package provides a simple Python interface to an efficient implementation of the Nemenman-Schafee-Bialek (NSB) algorithm, a parameter-free, Bayesian entropy estimator for discrete data.

Basic usage

The entropy function takes as input a vector of frequency counts (the observed frequencies for a set of classes or states) and returns an entropy estimate (in nats):

>>> counts
[7, 3, 5, 8, 9, 1, 3, 3, 1, 0, 2, 5, 2, 11, 4, 23, 5, 0, 8, 0]
>>> import ndd
>>> entropy_estimate = ndd.entropy(counts)
>>> entropy_estimate
2.623634344888532

Optionally, the uncertainty in the entropy estimate can be quantified by computing an approximation for the posterior standard deviation:

>>> entropy_estimate, std = ndd.entropy(counts, return_std=True)
>>> std
0.048675500725595504

Information measures

ndd provide functions for the estimation of entropic information measures (as linear combinations of single Bayesian entropy estimates):

• jensen_shannon_divergence

• kullback_leibler_divergence

• conditional_entropy

• mutual_information

• interaction_information

• coinformation

See the functions’ docstrings for details.

Where to get it

Install using pip:

pip3 install -U ndd

or directly from sources in github for the latest version of the code:

pip3 install git+https://github.com/simomarsili/ndd.git

In order to compile ndd, you will need numpy (>= 1.9) and a Fortran compiler installed on your machine. If you are using Debian or a Debian derivative such as Ubuntu, you can install the gfortran compiler using the following command:

sudo apt-get install gfortran

Running tests

Clone the repo, install tests requirements and run the tests with make:

git clone https://github.com/simomarsili/ndd.git
cd ndd
pip install .[test]
make test

Changes

1.4 (2019-05-20)

• Added kullback_leibler_divergence function.

1.3 (2019-05-08)

• For methods/functions working on data matrices:

  the default input is a p-by-n 2D array (n samples from p discrete variables, with different samples on different columns).

1.1 (2019-03-26)

Added:

• from_data

• mutual_information

• conditional_information

• interaction_information

• coinformation

1.0 (2019-03-19)

• Python3 only (>= 3.4)

0.9 (2019-01-15)

• Added jensen_shannnon_divergence function.

References

Some refs:

@article{wolpert1995estimating,
  title={Estimating functions of probability distributions from a finite set of samples},
  author={Wolpert, David H and Wolf, David R},
  journal={Physical Review E},
  volume={52},
  number={6},
  pages={6841},
  year={1995},
  publisher={APS}
}

@inproceedings{nemenman2002entropy,
  title={Entropy and inference, revisited},
  author={Nemenman, Ilya and Shafee, Fariel and Bialek, William},
  booktitle={Advances in neural information processing systems},
  pages={471--478},
  year={2002}
}

@article{nemenman2004entropy,
  title={Entropy and information in neural spike trains: Progress on the sampling problem},
  author={Nemenman, Ilya and Bialek, William and van Steveninck, Rob de Ruyter},
  journal={Physical Review E},
  volume={69},
  number={5},
  pages={056111},
  year={2004},
  publisher={APS}
}

@article{archer2013bayesian,
  title={Bayesian and quasi-Bayesian estimators for mutual information from discrete data},
  author={Archer, Evan and Park, Il Memming and Pillow, Jonathan W},
  journal={Entropy},
  volume={15},
  number={5},
  pages={1738--1755},
  year={2013},
  publisher={Multidisciplinary Digital Publishing Institute}
}

and interesting links:

• Sebastian Nowozin on Bayesian estimators

• Il Memming Park on discrete entropy estimators

Contributing

ndd is an OPEN Source Project so please help out by reporting bugs or forking and opening pull requests when possible.

License

Copyright (c) 2016-2019, Simone Marsili. All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS “AS IS” AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.