
 Description:
ITE can estimate
entropy
: Shannon entropy, Rényi entropy, Tsallis entropy (Havrda and Charvát entropy), complex entropy, Phientropy (fentropy), SharmaMittal entropy,mutual information
: generalized variance, kernel canonical correlation analysis, kernel generalized variance, HilbertSchmidt independence criterion, Shannon mutual information (total correlation, multiinformation), L2 mutual information, Rényi mutual information, Tsallis mutual information, copulabased kernel dependency, multivariate version of Hoeffding's Phi, SchweizerWolff's sigma and kappa, complex mutual information, CauchySchwartz quadratic mutual information, Euclidean distance based quadratic mutual information, distance covariance, distance correlation, approximate correntropy independence measure, chisquare mutual information (HilbertSchmidt norm of the normalized crosscovariance operator, squaredloss mutual information, mean square contingency),divergence
: KullbackLeibler 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), Jdistance (symmetrised KullbackLeibler divergence, J divergence), CauchySchwartz divergence, Euclidean distance based divergence, energy distance (specially the CramerVon Mises distance), JensenShannon divergence, JensenRényi divergence, K divergence, L divergence, certain fdivergences (CsiszárMorimoto divergence, AliSilvey distance), nonsymmetric Bregman distance (Bregman divergence), JensenTsallis divergence, symmetric Bregman distance, Pearson chi square divergence (chi square distance),association measures
, includingmeasures 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
: crossentropy,kernels on distributions
: expected kernel, Bhattacharyya kernel, probability product kernel, JensenShannon kernel, exponentiated JensenShannon kernel, JensenTsallis kernel, exponentiated JensenRenyi kernel(s), exponentiated JensenTsallis kernel(s),+some auxiliary quantities
: Bhattacharyya coefficient (Hellinger affinity).
ITE offers solution methods for
 Independent Subspace Analysis (ISA) and
 its extensions to different linear, controlled, post nonlinear, complex valued, partially observed models, as well as to systems with nonparametric source dynamics.
ITE is
 written in Matlab/Octave,
 multiplatform (tested extensively on Windows and Linux),
 free and open source (released under the GNU GPLv3(>=) license).
 Changes to previous version:
ITE has been accepted for publication in JMLR; citing information: added.
BlockMMD (maximum mean discrepancy) estimator: added.
'Extreme large' k in kNN based estimators: an overflow issue discovered + corrected.
+Some refactorization, documentation upgrade.
 BibTeX Entry: Download
 Corresponding Paper BibTeX Entry: Download
 URL: Project Homepage
 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
Other available revisons

Version Changelog Date 0.61 Explicit additive constant computation in generalized kNN based Renyi entropy estimators: enhancement suggestion has been added.
Analytical value computation of the exponentiated JensenRenyi kernel2: simplified.
February 8, 2015, 14:04:27 0.60 Quick test on the Tsallis divergence: introduced.
Pearson chi square divergence estimation in the exponential family (MLE + analytical formula): added.
June 3, 2014, 00:17:33 0.59 Adaptive partitioning based Shannon mutual information estimators: added.
Quick tests: updated to handle the new estimators.
May 16, 2014, 22:13:48 0.58 3way interaction indices based on the embedding of the (i) Lancaster interaction and (ii) 'joint  product of the marginals' signed measures to a RKHS: added.
Quick tests: updated to cover the new estimators.
April 29, 2014, 22:08:50 0.57 KullbackLeibler divergence estimation based on maximum likelihood estimation + analytical formula in the chosen exponential family: added.
A new sampling based entropy estimator with KDE correction on the left/right sides: added.
Quick tests: updated with the new estimators.
April 10, 2014, 18:35:22 0.56 Distribution regression (supervised entropy learning, aerosol optical depth prediction based on satellite images): added.
MMD distance computation based on Ustatistics, expected kernel: upgraded to cover new kernels (exponential, Cauchy, Matern, polynomial, rational quadratic, inverse multiquadratic).
March 27, 2014, 22:06:54 0.55 Shannon entropy and crossentropy estimation based on maximum likelihood estimation + analytical formula in the chosen exponential family: added.
Quick tests: updated with the new estimators.
March 8, 2014, 00:18:00 0.54 Renyi and Tsallis entropy estimation based on maximum likelihood estimation + analytical formula in the exponential family: added.
Quick tests: updated according to the new estimators.
February 24, 2014, 18:28:32 0.53 fdivergence estimation based on secondorder Taylor expansion + Pearson chi square divergence: added.
Shannon mutual information estimation based on KL divergence: added.
Quick tests: updated with the new estimators.
February 2, 2014, 14:04:19 0.52 SharmaMittal divergence estimation: added using (i) maximum likelihood estimation + analytical formula in the exponential family, (ii) knearest neighbors.
Quick test for (i) SharmaMittal divergence, (ii) Shannon mutual information: added.
Normal variables: added to the Pearson chi square divergence quick test.
January 10, 2014, 00:02:47 0.51 ITE has been accepted for publication in JMLR; citing information: added.
BlockMMD (maximum mean discrepancy) estimator: added.
'Extreme large' k in kNN based estimators: an overflow issue discovered + corrected.
+Some refactorization, documentation upgrade.
December 29, 2013, 17:36:00 0.50 Entropy and KullbackLeibler divergence estimation based on power spectral density representation and Szegő's theorem: added.
Different noisy examples have been added to the image registration quick test.
December 18, 2013, 20:53:28 0.49 MMD (maximum mean discrepancy) estimation based on U and Vstatistics: incomplete Cholesky decomposition based accelerations added.
Refactorization; improved navigation in the documentation.
December 1, 2013, 16:44:15 0.48 SharmaMittal entropy estimation based on
knearest neighbors (S={k}): added.
maximum likehood estimation + analytical value in the exponential family: added.
November 11, 2013, 19:26:39 0.47 Chisquare mutual information estimation based on Pearson chisquare divergence: added.
Shannon entropy estimation based on an alternative linearly corrected spacing method: added.
November 1, 2013, 19:29:12 0.46 Phientropy (fentropy) estimation based on the spacing method: added.
Pearson chi square divergence (chi square distance) estimation based on knearest neighbors: added.
October 21, 2013, 19:31:52 0.45 Exponentiated JensenTsallis kernel1 estimation based on Tsallis entropy: added.
Exponentiated JensenTsallis kernel2 estimation based on JensenTsallis divergence: added.
October 9, 2013, 21:44:21 0.44 Exponentiated JensenRenyi kernel1 estimation based on Renyi entropy: added.
Exponentiated JensenRenyi kernel2 estimation based on JensenRenyi divergence: added.
October 1, 2013, 18:16:38 0.43 Exponentiated JensenShannon kernel estimation: added.
JensenTsallis kernel estimation: added.
September 20, 2013, 19:56:45 0.42 Highlevel information theoretical estimators: 'eval' changed to 'function handles'  speeds up computations.
Cost object initialization: now allows setting field values (alpha, number of kNNs, ...) through its argument. => possibility to override default values, automatic inheritence in meta estimators.
Quick tests introduced: consistency of the estimators (analytical vs. estimated value), positive semidefiniteness of Gram matrices determined by distribution kernels, image registration.
Refactorization; documentation: improved.
September 7, 2013, 16:46:42 0.41 Probability product kernel estimation based on knearest neighbors: added,
JensenShannon kernel estimation: added.
July 12, 2013, 21:33:42 0.40 Bhattacharyya kernel estimation based on knearest neighbors: added,
Expected kernel estimation: added,
Kernel on distributions (K) object type: added.
June 23, 2013, 13:13:27 0.39 Symmetric Bregman distance estimation based on nonsymmetric Bregman distance: added,
Symmetric Bregman distance estimation using the knearest neighbor method: added.
June 12, 2013, 13:12:52 0.38 JensenTsallis divergence estimation: added,
Bregman distance estimation: added.
June 1, 2013, 10:20:00 0.37 K divergence estimation: added,
L divergence estimation: added,
kNN squared distance computation: refined.
May 12, 2013, 15:35:39 0.36 JensenRényi divergence estimation: added,
JensenShannon divergence estimation: added.
April 26, 2013, 18:45:27 0.35 An alternative Jacobi optimization based ICA solution with general entropy/mutual information estimators: added; The method extends the RADICAL ICA scheme to general objectives.
April 2, 2013, 10:37:51 0.34 Jacobi optimization based ICA solution with general entropy/mutual information estimators: added. The method extends the SWICA scheme to general objectives.
March 22, 2013, 11:41:05 0.33 Two onedimensional Shannon entropy estimators based on the maximum entropy method: added.
March 6, 2013, 09:44:47 0.32 ICA and ISA structures: introduced for unified treatment of the estimators. It will also enable embedding of general ICA optimization algorithms such as the Jacobi method.
'stepwiseLS' mAR estimator: deleted.
'kdpee.c': MSVC does not provide log2. A more elegant solution: added.
February 25, 2013, 12:42:40 0.31 EASI (equivariant adaptive separation via independence) real/complex ICA method: added.
Adaptive (kd) partitioning based Shannon entropy estimation: added.
February 9, 2013, 11:31:39 0.30 Upper tail dependence via conditional Spearman's rho: added.
Multivariate conditional version of Spearman's rho weighting the lower tail: added.
January 25, 2013, 15:11:25 0.29 Lower tail dependence via conditional Spearman's rho: added.
Multivariate conditional version of Spearman's rho weighting the lower tail: added.
January 13, 2013, 11:38:17 0.28 Multivariate extension of Blomqvist's beta (medial correlation coefficient): added.
Average pairwise Spearman's rho: added.
January 2, 2013, 22:51:22 0.27 Approximate correntropy independence measure estimator: added.
Correntropy induced metric, centered correntropy induced metric estimators: added.
Correntropy, centered correntropy, correntropy coefficient estimators: added.
Handling of identically constant random variables in distance correlation computation: included.
December 28, 2012, 14:41:57 0.26 Distance covariance estimation via HSIC (HilbertSchmidt independence criterion): added.
Energy distance estimation via MMD (maximum mean discrepancy): added.
Energy distance estimation: added.
We computed the square of distance correlation: sqrt included.
December 22, 2012, 14:12:33 0.25 Distance covariance, distance correlation estimation: added.
December 15, 2012, 10:20:06 0.24 MMD (maximum mean discrepancy) estimation based on U and Vstatistics: added.
December 12, 2012, 12:16:05 0.23 Three multivariate extensions of Spearman's rho (Spearman's rank correlation coefficient): added.
Association (A) cost object type: added.
December 7, 2012, 18:33:26 0.22 CauchySchwartz and Euclidean distance based divergence estimators: added.
CauchySchwartz and Euclidean distance based quadratic mutual information estimators: added.
December 1, 2012, 13:33:31 0.21 KullbackLeibler divergence estimator based on crossentropy and entropy: added.
Crossentropy estimation based on knearest neighbors: added.
Cross cost object type: added.
November 25, 2012, 20:56:32 0.20 Two Shannon entropy estimators based on the distance (KL divergence) from the uniform/Gaussian distributions: added.
Shannon entropy estimator based on Voronoi regions: added.
November 21, 2012, 13:55:09 0.19 Two knearest neighbor based KullbackLeibler divergence estimators: added.
compute_CDSS.cpp: 'sqrt(T)' > 'sqrt(double(T))', to increase compatibility with compilers.
November 21, 2012, 13:47:05 0.18 8 sample spacing based 1d Shannon/Rényi entropy estimators: added.
November 10, 2012, 12:53:37 0.17  Edgeworth expansion based Shannon entropy estimator: accelerated (C++ alternative).
 'Tsallis entropy < Renyi entropy' meta estimator: added.
November 6, 2012, 22:18:43 0.16  Edgeworth expansion based Shannon entropy estimator: added.
 Lookup table for the underlying H/I/D estimation formulas: added (documentation).
November 2, 2012, 16:03:25 0.15 The Hellinger and Bhattacharyya distances are now available in ITE. They can be estimated via knearest neighbor methods.
A '/'>'*' typo: corrected in 'DL2_kNN_k_estimation.m'.
October 29, 2012, 17:27:28 0.14  MonteCarlo simulation to compute the additive constants in Rényi entropy estimation: added.
 some accelerations/compatibility enhancements: performed.
October 29, 2012, 12:31:34 0.13  Tsallis entropy is now available in ITE. It can be estimated via knearest neighbors.
 A '/'>'*' typo: corrected in 'HRenyi_kNN_k_estimation.m'.
October 27, 2012, 22:14:18 0.12  SchweizerWolff's sigma and kappa: added.
 Hoeffding's Phi computation: scaledup.
October 27, 2012, 21:21:27 0.11 multivariate version of Hoeffding's Phi: added.
October 20, 2012, 23:30:17 0.1 Initial Announcement on mloss.org.
October 11, 2012, 07:47:43
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