ITE (Information Theoretical Estimators) Toolbox

News: ITE has been

ITE is capable of estimating many different variants of entropy, mutual information, divergence, association measures, cross quantities, and kernels on distributions. Thanks to its highly modular design, ITE supports additionally

  • the combinations of the estimation techniques,
  • the easy construction and embedding of novel information theoretical estimators, and
  • their immediate application in information theoretical optimization problems.

ITE is

  • written in Matlab/Octave,
  • multi-platform (tested extensively on Windows and Linux),
  • free and open source (released under the GNU GPLv3(>=) license).

ITE can estimate

  • entropy (H): Shannon entropy, Rényi entropy, Tsallis entropy (Havrda and Charvát entropy), complex entropy, Phi-entropy (f-entropy), Sharma-Mittal entropy,
  • mutual information (I): generalized variance, kernel canonical correlation analysis, kernel generalized variance, Hilbert-Schmidt independence criterion, Shannon mutual information (total correlation, multi-information), L2 mutual information, Rényi mutual information, Tsallis mutual information, copula-based kernel dependency, multivariate version of Hoeffding's Phi, Schweizer-Wolff's sigma and kappa, complex mutual information, Cauchy-Schwartz quadratic mutual information, Euclidean distance based quadratic mutual information, distance covariance, distance correlation, approximate correntropy independence measure, chi-square mutual information (Hilbert-Schmidt norm of the normalized cross-covariance operator, squared-loss mutual information, mean square contingency),
  • divergence (D): Kullback-Leibler divergence (relative entropy, I directed divergence), L2 divergence, Rényi divergence, Tsallis divergence, Hellinger distance, Bhattacharyya distance, maximum mean discrepancy (kernel distance), J-distance (symmetrised Kullback-Leibler divergence, J divergence), Cauchy-Schwartz divergence, Euclidean distance based divergence, energy distance (specially the Cramer-Von Mises distance), Jensen-Shannon divergence, Jensen-Rényi divergence, K divergence, L divergence, certain f-divergences (Csiszár-Morimoto divergence, Ali-Silvey distance), non-symmetric Bregman distance (Bregman divergence), Jensen-Tsallis divergence, symmetric Bregman distance, Pearson chi square divergence (chi square distance),
  • association measures (A), including measures of concordance: multivariate extensions of Spearman's rho (Spearman's rank correlation coefficient, grade correlation coefficient), correntropy, centered correntropy, correntropy coefficient, correntropy induced metric, centered correntropy induced metric, multivariate extension of Blomqvist's beta (medial correlation coefficient), multivariate conditional version of Spearman's rho, lower/upper tail dependence via conditional Spearman's rho,
  • cross quantities (C): cross-entropy,
  • kernels on distributions (K): expected kernel, Bhattacharyya kernel, probability product kernel, Jensen-Shannon kernel, exponentiated Jensen-Shannon kernel, exponentiated Jensen-Renyi kernel(s), Jensen-Tsallis kernel, exponentiated Jensen-Tsallis kernel(s), and
  • +some auxiliary quantities: Bhattacharyya coefficient (Hellinger affinity).

ITE offers

  • solution methods for (i) Independent Subspace Analysis (ISA), and (ii) its extensions to different linear-, controlled-, post nonlinear-, complex valued-, partially observed models, as well as to systems with nonparametric source dynamics,
  • several consistency tests (analytical vs estimated value), and
  • a further demonstration in image registration.


  • the evolution of the ITE code is briefly summarized in CHANGELOG.txt.
  • you can become a Follower to be always up-to-date with ITE.
  • if you have a H/I/D/A/C/K estimator/subtask solver [with a GPLv3(>=)-compatible license, such as GPLv3 or GPLv3(>=)] that you would like to be embedded into ITE, feel free to contact me.

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

Download the latest release: