Information Theoretical Estimators (ITE) in Python


  • is the redesigned, Python implementation of the Matlab/Octave ITE toolbox.
  • can estimate numerous entropy, mutual information, divergence, association measures, cross quantities, and kernels on distributions.
  • can be used to solve information theoretical optimization problems in a high-level way.
  • comes with several demos.
  • is free and open source: GNU GPLv3(>=).

Estimated quantities:

  • entropy (H): Shannon entropy, Rényi entropy, Tsallis entropy (Havrda and Charvát entropy), Sharma-Mittal entropy, Phi-entropy (f-entropy).
  • mutual information (I): Shannon mutual information (total correlation, multi-information), Rényi mutual information, Tsallis mutual information, chi-square mutual information (squared-loss mutual information, mean square contingency), L2 mutual information, copula-based kernel dependency, kernel canonical correlation analysis, kernel generalized variance, multivariate version of Hoeffding's Phi, Hilbert-Schmidt independence criterion, distance covariance, distance correlation, Lancaster three-variable interaction.
  • divergence (D): Kullback-Leibler divergence (relative entropy, I directed divergence), Rényi divergence, Tsallis divergence, Sharma-Mittal divergence, Pearson chi-square divergence (chi-square distance), Hellinger distance, L2 divergence, f-divergence (Csiszár-Morimoto divergence, Ali-Silvey distance), maximum mean discrepancy (kernel distance, current distance), energy distance (specifically the Cramer-Von Mises distance), Bhattacharyya distance, non-symmetric Bregman distance (Bregman divergence), symmetric Bregman distance, J-distance (symmetrised Kullback-Leibler divergence, J divergence), K divergence, L divergence, Jensen-Shannon divergence, Jensen-Rényi divergence, Jensen-Tsallis divergence.
  • association measures (A): multivariate extensions of Spearman's rho (Spearman's rank correlation coefficient, grade correlation coefficient), multivariate conditional version of Spearman's rho, lower and upper tail dependence via conditional Spearman's rho.
  • cross quantities (C): cross-entropy,
  • kernels on distributions (K): expected kernel (summation kernel, mean map kernel, set kernel, multi-instance kernel, ensemble kernel; specific convolution kernel), probability product kernel, Bhattacharyya kernel (Bhattacharyya coefficient, Hellinger affinity), Jensen-Shannon kernel, Jensen-Tsallis kernel, exponentiated Jensen-Shannon kernel, exponentiated Jensen-Rényi kernels, exponentiated Jensen-Tsallis kernels.
  • conditional entropy (condH): conditional Shannon entropy.
  • conditional mutual information (condI): conditional Shannon mutual information.

Citing: If you use the ITE toolbox in your research, please cite it [.bib].

Download the latest release:

Note: the evolution of the code is briefly summarized in CHANGELOG.txt.

ITE mailing list: You can sign up here.

Follow ITE: on Bitbucket, on Twitter.

ITE applications: Wiki. Feel free to add yours.