Mutual Information Estimation via $f$-Divergence and Data Derangements

TL;DR

This paper introduces a new mutual information estimator based on $f$-divergence and derangements, achieving better bias-variance trade-off, higher accuracy, and lower complexity compared to existing neural methods.

Contribution

It proposes a novel discriminative mutual information estimator using $f$-divergence and derangements, improving accuracy and efficiency over prior neural estimators.

Findings

Higher accuracy than state-of-the-art methods

Lower complexity in estimation process

Better bias-variance trade-off

Abstract

Estimating mutual information accurately is pivotal across diverse applications, from machine learning to communications and biology, enabling us to gain insights into the inner mechanisms of complex systems. Yet, dealing with high-dimensional data presents a formidable challenge, due to its size and the presence of intricate relationships. Recently proposed neural methods employing variational lower bounds on the mutual information have gained prominence. However, these approaches suffer from either high bias or high variance, as the sample size and the structure of the loss function directly influence the training process. In this paper, we propose a novel class of discriminative mutual information estimators based on the variational representation of the $f$-divergence. We investigate the impact of the permutation function used to obtain the marginal training samples and present a novel architectural solution based on derangements. The proposed estimator is flexible since it exhibits an excellent bias/variance trade-off. The comparison with state-of-the-art neural estimators, through extensive experimentation within established reference scenarios, shows that our approach offers higher accuracy and lower complexity.