Flow-based Variational Mutual Information: Fast and Flexible Approximations

Caleb Dahlke, Jason Pacheco

Keywords: Mutual Information, Variational Methods, Normalizing Flows, Bayesian Optimal Experimental Design

TL;DR: We introduce two new flow-based variational Mutual Information estimations that are comparable in expressiveness to critic-based methods, such as MINE or InfoNCE, but can also approximate large MI

Abstract: Mutual Information (MI) is a fundamental measure of dependence between random variables, but its practical application is limited because it is difficult to calculate in many circumstances. Variational methods offer one approach by introducing an approximate distribution to create various bounds on MI, which in turn is an easier optimization problem to solve. In practice, the variational distribution chosen is often a Gaussian, which is convenient but lacks flexibility in modeling complicated distributions. In this paper, we introduce new classes of variational estimators based on Normalizing Flows that extend the previous Gaussian-based variational estimators. Our new estimators maintain many of the same theoretical guarantees while simultaneously enhancing the expressivity of the variational distribution. We experimentally verify that our new methods are effective on large MI problems where discriminative-based estimators, such as MINE and InfoNCE, are fundamentally limited. Furthermore, we compare against a diverse set of benchmarking tests to show that the flow-based estimators often perform as well, if not better, than the discriminative-based counterparts. Finally, we demonstrate how these estimators can be effectively utilized in the Bayesian Optimal Experimental Design setting for online sequential decision making.

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

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Submission Number: 11672