simomarsili/ndd
Fork: 3 Star: 37 (更新于 1970-01-01 00:00:00)
license: BSD-3-Clause
Language: Python .
Bayesian entropy estimation in Python - via the Nemenman-Schafee-Bialek algorithm
最后发布版本: v1.10.6 ( 2021-01-04 20:14:17)
==================================================== ndd - Bayesian entropy estimation from discrete data
.. image:: https://badge.fury.io/py/ndd.svg :target: https://badge.fury.io/py/ndd .. image:: https://travis-ci.com/simomarsili/ndd.svg?branch=master :target: https://travis-ci.com/simomarsili/ndd
ndd
is a Python package for Bayesian entropy estimation from discrete
data. ndd
provides the ndd.entropy
function, a Bayesian replacement
for the scipy.stats.entropy
function from the SciPy library,
based on an efficient implementation of the
Nemenman-Schafee-Bialek (NSB) algorithm <https://arxiv.org/abs/physics/0108025>
_.
Remarkably, the NSB algorithm allows entropy estimation when the number of
samples is much smaller than the number of classes with non-zero probability.
Basic usage
The entropy
function takes as input a vector of frequency counts
(the observed frequencies for a set of classes or states) and an alphabet size
(the number of classes with non-zero probability, including unobserved classes)
and returns an entropy estimate (in nats)::
import ndd counts = [4, 12, 4, 5, 3, 1, 5, 1, 2, 2, 2, 2, 11, 3, 4, 12, 12, 1, 2] ndd.entropy(counts, k=100) 2.8060922529931225
The uncertainty in the entropy estimate can be quantified using the
posterior standard deviation (see Eq. 13 in Archer 2013 <https://pillowlab.princeton.edu/pubs/Archer13_MIestim_Entropy.pdf>
_) ::
ndd.entropy(counts, k=100, return_std=True) (2.8060922529931225, 0.11945501149743358)
If the alphabet size is unknown or countably infinite, the k
argument can
be omitted and the entropy
function will either use an upper bound estimate
for k
, or switch to the asymptotic NSB estimator for strongly undersampled
distributions (Equations 29, 30 in
Nemenman 2011 <https://nemenmanlab.org/~ilya/images/c/c1/Nemenman_2011b.pdf>
_) ::
import ndd counts = [4, 12, 4, 5, 3, 1, 5, 1, 2, 2, 2, 2, 11, 3, 4, 12, 12, 1, 2] ndd.entropy(counts) # k is omitted 2.8130746489179046
Where to get it
conda
The easiest way to install ndd
is via the conda
package manager.
Packages are provided on the conda-forge
Anaconda Cloud channel for Linux,
OS X, and Win platforms.
Install the latest stable release using conda
with::
conda install --channel conda-forge ndd
pip
Install using pip with::
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 build ndd
with pip
, you will need numpy
(>= 1.13) 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
On Windows, you can use the gfortran compiler from the
MinGW-w64 <https://sourceforge.net/projects/mingw-w64/files>
_ project
(direct link <https://sourceforge.net/projects/mingw-w64/files/latest/download>
_
to the installer).
Changes
v1.10.5
Added ndd
to the anaconda conda-forge
channel.
v1.10
Changed:
the signature of the entropy
function is:::
entropy(nk, k=None, estimator=None, return_std=False)
v1.9 Changed:
if argument k
is omitted, the entropy
function will guess a
reasonable alphabet size and select the best estimator for the sampling
regime.
v.1.8.3 Fixed:
integration for huge cardinalities
v1.8 Added:
full Bayesian error estimate (from direct computation of the posterior variance of the entropy)
v1.7 Changed:
estimation is much faster (removed unnecessary checks on input counts)
entropy()
function needs cardinality k
for the default (NSB)
estimator
v1.6.1 Changed: Fixed numerical integration for large alphabet sizes.
v1.6 Changed:
The signature of the entropy
function has been changed to allow
arbitrary entropy estimators. The new signature is::
entropy(pk, k=None, estimator='NSB', return_std=False)
The available estimators are::
>>> import ndd
>>> ndd.entropy_estimators
['Plugin', 'MillerMadow', 'NSB', 'AsymptoticNSB', 'Grassberger']
Check the function docstring for details.
Added:
- MillerMadow estimator class
- AsymptoticNSB estimator class
- Grassberger estimator class
v1.5 For methods/functions working on data matrices: the default input is a n-by-p 2D array (n samples from p discrete variables, with different samples on different rows). Since release 1.3, the default was a transposed (p-by-n) data matrix. The behavior of functions taking frequency counts as input (e.g. the entropy function) is unchanged. v1.4 Added the kullback_leibler_divergence function. v1.1 Added:
* *from_data*
* *mutual_information*
* *conditional_information*
* *interaction_information*
* *coinformation*
v1.0
Drop support for Python < 3.4.
v0.9
Added the 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{paninski2003estimation, title={Estimation of entropy and mutual information}, author={Paninski, Liam}, journal={Neural computation}, volume={15}, number={6}, pages={1191--1253}, year={2003}, publisher={MIT Press} }
@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{nemenman2011coincidences, title={Coincidences and estimation of entropies of random variables with large cardinalities}, author={Nemenman, Ilya}, journal={Entropy}, volume={13}, number={12}, pages={2013--2023}, year={2011}, publisher={Molecular Diversity Preservation International} }
@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} }
@article{archer2014bayesian, title={Bayesian entropy estimation for countable discrete distributions}, author={Archer, Evan and Park, Il Memming and Pillow, Jonathan W}, journal={The Journal of Machine Learning Research}, volume={15}, number={1}, pages={2833--2868}, year={2014}, publisher={JMLR. org} }
and interesting links:
-
Sebastian Nowozin on Bayesian estimators <http://www.nowozin.net/sebastian/blog/estimating-discrete-entropy-part-3.html>
_ -
Il Memming Park on discrete entropy estimators <https://memming.wordpress.com/2014/02/09/a-guide-to-discrete-entropy-estimators/>
_
Contributing
ndd is an OPEN Source Project so please help out by reporting bugs <https://github.com/simomarsili/ndd>
_ 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:
-
Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
-
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.
-
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.
最近版本更新:(数据更新于 1970-01-01 00:00:00)
2021-01-04 20:14:17 v1.10.6
2020-10-20 23:26:01 v1.10.5
2020-10-20 23:15:41 v1.10.4
2020-10-20 04:38:21 v1.10.1
2020-10-09 21:31:34 v1.10
2020-09-22 01:55:01 v1.9.2
2020-07-07 18:36:34 v1.9.1
2020-06-27 05:02:14 v1.9
2020-06-25 07:58:45 v1.8.4
2020-06-17 00:19:24 v1.8.3
主题(topics):
bayes, categorical-data, entropy, jensen-shannon-divergence, python
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