MINDE: Mutual Information Neural Diffusion Estimation

TL;DR

This paper introduces MINDE, a novel neural diffusion-based method for estimating mutual information and entropy between random variables, demonstrating superior accuracy and consistency over existing techniques.

Contribution

The paper presents a new MI estimation approach using score-based diffusion models derived from the Girsanov theorem, enabling more accurate and consistent measurements.

Findings

Outperforms existing MI estimation methods on challenging distributions

Passes MI self-consistency tests such as data processing and additivity

Provides a unified framework for estimating MI and entropy using diffusion models

Abstract

In this work we present a new method for the estimation of Mutual Information (MI) between random variables. Our approach is based on an original interpretation of the Girsanov theorem, which allows us to use score-based diffusion models to estimate the Kullback Leibler divergence between two densities as a difference between their score functions. As a by-product, our method also enables the estimation of the entropy of random variables. Armed with such building blocks, we present a general recipe to measure MI, which unfolds in two directions: one uses conditional diffusion process, whereas the other uses joint diffusion processes that allow simultaneous modelling of two random variables. Our results, which derive from a thorough experimental protocol over all the variants of our approach, indicate that our method is more accurate than the main alternatives from the literature, especially for challenging distributions. Furthermore, our methods pass MI self-consistency tests, including data processing and additivity under independence, which instead are a pain-point of existing methods.