Non-parametric Entropy Estimation Toolbox

This package contains Python code implementing several entropy estimation functions for both discrete and continuous variables. Information theory provides a model-free way find structure in complex systems, but difficulties in estimating these quantities has traditionally made these techniques infeasible. This package attempts to allay these difficulties by making modern state-of-the-art entropy estimation methods accessible in a single easy-to-use python library.

The implementation is very simple. It only requires that numpy/scipy be installed. It includes estimators for entropy, mutual information, and conditional mutual information for both continuous and discrete variables. Additionally it includes a KL Divergence estimator for continuous distributions and mutual information estimator between continuous and discrete variables along with some non-parametric tests for evaluating estimator performance.

The main documentation is in npeet_doc.pdf. It includes description of functions, references, implementation details, and technical discussion about the difficulties in estimating entropies. The code is available here. It requires scipy 0.12 or greater. This package is mainly geared to estimating information-theoretic quantities for continuous variables in a non-parametric way. If your primary interest is in discrete entropy estimation, particularly with undersampled data, please see this package.

Example installation and usage:

git clone https://github.com/gregversteeg/NPEET.git

>>> import entropy_estimators as ee
>>> x = [[1.3],[3.7],[5.1],[2.4],[3.4]]
>>> y = [[1.5],[3.32],[5.3],[2.3],[3.3]]
>>> ee.mi(x,y)
Out: 0.168

Another example:

import numpy as np
import entropy_estimators as ee

my_data = np.genfromtxt('my_file.csv', delimiter=',')  # If you look in the documentation, there is a way to skip header rows and other things

x = my_data[:,[5]].tolist()
y = my_data[:,[9]].tolist()
z = my_data[:,[15,17]].tolist()
print ee.cmi(x, y, z)
print ee.shuffle_test(ee.cmi, x, y, z, ci=0.95, ns=1000)

This prints the mutual information between column 5 and 9, conditioned on columns 15 and 17. You can also use the function shuffle_test to return confidence intervals for any estimator. Shuffle_test returns the mean CMI under the null hypothesis (CMI=0), and 95% confidence intervals, estimated using 1000 random permutations of the data. Note that we converted the numpy arrays to lists! The current version really works only on python lists (lists of lists actually, as in the first example.

See documentation for references on all implemented estimators.

			A Kraskov, H Stögbauer, P Grassberger. 
			http://pre.aps.org/abstract/PRE/v69/i6/e066138
			Estimating Mutual Information
			PRE 2004.

			Greg Ver Steeg and Aram Galstyan 
			http://lanl.arxiv.org/abs/1208.4475
			Information-Theoretic Measures of Influence Based on Content Dynamics
			WSDM, 2013.

			Greg Ver Steeg and Aram Galstyan 
			http://arxiv.org/abs/1110.2724 
			Information Transfer in Social Media
			WWW, 2012.

The non-parametric estimators actually fare poorly for variables with strong relationships. See the following paper and the improved code available at https://github.com/BiuBiuBiLL/NPEET_LNC

			Shuyang Gao, Greg Ver Steeg and Aram Galstyan 
			http://arxiv.org/abs/1411.2003
			Efficient Estimation of Mutual Information for Strongly Dependent Variables
			AISTATS, 2015.