Understanding the Limitations of Variational Mutual Information Estimators

TL;DR

This paper analyzes the limitations of neural network-based variational mutual information estimators, revealing their potential for high variance and proposing a new estimator with better bias-variance trade-offs.

Contribution

It provides a theoretical analysis of variance issues in existing estimators and introduces a new estimator that improves variance reduction in mutual information estimation.

Findings

Existing estimators can have exponentially growing variance.

Current estimators often violate basic MI properties like data processing.

The proposed estimator shows improved bias-variance trade-offs in benchmarks.

Abstract

Variational approaches based on neural networks are showing promise for estimating mutual information (MI) between high dimensional variables. However, they can be difficult to use in practice due to poorly understood bias/variance tradeoffs. We theoretically show that, under some conditions, estimators such as MINE exhibit variance that could grow exponentially with the true amount of underlying MI. We also empirically demonstrate that existing estimators fail to satisfy basic self-consistency properties of MI, such as data processing and additivity under independence. Based on a unified perspective of variational approaches, we develop a new estimator that focuses on variance reduction. Empirical results on standard benchmark tasks demonstrate that our proposed estimator exhibits improved bias-variance trade-offs on standard benchmark tasks.