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Estimating mutual information (MI) from samples is a fundamental problem instatistics, machine learning, and data analysis. Recently it was shown that apopular class of non-parametric MI estimators perform very poorly for stronglydependent variables and have sample complexity that scales exponentially withthe true MI. This undesired behavior was attributed to the reliance of thoseestimators on local uniformity of the underlying (and unknown) probabilitydensity function. Here we present a novel semi-parametric estimator of mutualinformation, where at each sample point, densities are {\em locally}approximated by a Gaussians distribution. We demonstrate that the estimator isasymptotically unbiased. We also show that the proposed estimator has asuperior performance compared to several baselines, and is able to accuratelymeasure relationship strengths over many orders of magnitude.

Estimating Mutual Information by Local Gaussian Approximation