Estimating Mutual Information by Local Gaussian Approximation

Estimating Mutual Information by Local Gaussian Approximation Report Title Estimating mutual information (MI) from samples is a fundamental problem in statistics, machine learning, and data analysis. Recently it was shown that a popular class of non-parametric MI estimators perform very poorly for strongly dependent variables and have sample complexity that scales exponentially with the true MI. This undesired behavior was attributed to the reliance of those estimators on local uniformity of the underlying (and unknown) probability density function. Here we present a novel semi-parametric estimator of mutual information, where at each sample point, densities are {\em locally} approximated by a Gaussians distribution. We demonstrate that the estimator is asymptotically unbiased. We also show that the proposed estimator has a superior performance compared to several baselines, and is able to accurately measure relationship strengths over many orders of magnitude. Conference Name: The 31st Conference on Uncertainty in Artificial Intelligence Conference Date: July 13, 2015 Estimating Mutual Information by Local Gaussian Approximation Shuyang Gao Information Sciences Institute University of Southern California [email protected] Greg Ver Steeg Information Sciences Institute University of Southern California [email protected] Aram Galstyan Information Sciences Institute University of Southern California [email protected]