MINDE: Mutual Information Neural Diffusion Estimation
This work addresses the challenge of reliable mutual information estimation for researchers in machine learning and statistics, offering a novel approach that overcomes limitations of current methods.
The authors tackled the problem of estimating mutual information between random variables by introducing a new method based on score-based diffusion models and the Girsanov theorem, resulting in improved accuracy over existing alternatives, especially for challenging distributions, and passing key self-consistency tests.
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.