Efficient Estimation of Mutual Information for Strongly Dependent Variables

We demonstrate that a popular class of nonparametric mutual information (MI) estimators based on k-nearest-neighbor graphs requires number of samples that scales exponentially with the true MI. Consequently, accurate estimation of MI between two strongly dependent variables is possible only for prohibitively large sample size. This important yet overlooked shortcoming of the existing estimators is due to their implicit reliance on local uniformity of the underlying joint distribution. We introduce a new estimator that is robust to local non-uniformity, works well with limited data, and is able to capture relationship strengths over many orders of magnitude. We demonstrate the superior performance of the proposed estimator on both synthetic and real-world data.Comment: 13 pages, to appear in International Conference on Artificial Intelligence and Statistics (AISTATS) 201

Fast Multidimensional Entropy Estimation by k-d Partitioning

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Information Theoretical Estimators Toolbox

We present ITE (information theoretical estimators) a free and open source, multi-platform, Matlab/Octave toolbox that 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 (i) the combinations of the estimation techniques, (ii) the easy construction and embedding of novel information theoretical estimators, and (iii) their immediate application in information theoretical optimization problems. ITE also includes a prototype application in a central problem class of signal processing, independent subspace analysis and its extensions.Comment: 5 pages; ITE toolbox: https://bitbucket.org/szzoli/ite