Beyond Normal: On the Evaluation of Mutual Information Estimators

Paweł Czyż, Frederic Grabowski, Julia E Vogt, Niko Beerenwinkel, Alexander Marx

Keywords: Mutual Information, Invariance, Benchmark, Geometric Machine Learning

TL;DR: To benchmark classical and neural mutual information estimators, we develop a rich set of distributions easy to sample from and with known ground-truth mutual information.

Abstract: Mutual information is a general statistical dependency measure which has found applications in representation learning, causality, domain generalization and computational biology. However, mutual information estimators are typically evaluated on simple families of probability distributions, namely multivariate normal distribution and selected distributions with one-dimensional random variables. In this paper, we show how to construct a diverse family of distributions with known ground-truth mutual information and propose a language-independent benchmarking platform for mutual information estimators. We discuss the general applicability and limitations of classical and neural estimators in settings involving high dimensions, sparse interactions, long-tailed distributions, and high mutual information. Finally, we provide guidelines for practitioners on how to select appropriate estimator adapted to the difficulty of problem considered and issues one needs to consider when applying an estimator to a new data set.

Submission Number: 5194