Project details for Information Theoretical Estimators

Screenshot JMLR Information Theoretical Estimators 0.61

by szzoli - February 8, 2015, 14:04:27 CET [ Project Homepage BibTeX BibTeX for corresponding Paper Download ]

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ITE can estimate

  • entropy: Shannon entropy, Rényi entropy, Tsallis entropy (Havrda and Charvát entropy), complex entropy, Phi-entropy (f-entropy), Sharma-Mittal entropy,

  • mutual information: 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: Kullback-Leibler divergence (relative entropy, I directed divergence), L2 divergence, Rényi divergence, Tsallis divergence, Hellinger distance, Bhattacharyya distance, maximum mean discrepancy (kernel distance, an integral probability metric), 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, f-divergence (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), Sharma-Mittal divergence,

  • association measures, 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: cross-entropy,

  • kernels on distributions: expected kernel (summation kernel, mean map kernel, set kernel, multi-instance kernel, ensemble kernel; special convolution kernel), Bhattacharyya kernel (Bhattacharyya coefficient, Hellinger affinity), probability product kernel, Jensen-Shannon kernel, exponentiated Jensen-Shannon kernel, Jensen-Tsallis kernel, exponentiated Jensen-Renyi kernel(s), exponentiated Jensen-Tsallis kernel(s).

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),

  • illustrations for information theoretical image registration, and

  • distribution regression with applications in (i) supervised entropy learning and (ii) aerosol optical depth prediction based on satellite images.

ITE is

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

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Changes to previous version:
  • Explicit additive constant computation in generalized kNN based Renyi entropy estimators: enhancement suggestion has been added.

  • Analytical value computation of the exponentiated Jensen-Renyi kernel-2: simplified.

BibTeX Entry: Download
Corresponding Paper BibTeX Entry: Download
Supported Operating Systems: Linux, Windows
Data Formats: Matlab, Octave
Tags: Entropy, Mutual Information, Divergence, Independent Subspace Analysis, Separation Principles, Independent Process Analysis, Association Measure, Measure Of Concordance, Measure Of Independence, Nonpa
Archive: download here


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