Optimizing Likelihoods via Mutual Information: Bridging Simulation-Based Inference and Bayesian Optimal Experimental Design

TL;DR

This paper introduces a novel approach connecting simulation-based inference and Bayesian experimental design through mutual information bounds, enabling improved inference and experimental resource utilization.

Contribution

It establishes a theoretical link allowing BOED to enhance SBI, and demonstrates practical benefits in real-world epidemiology and biology models.

Findings

Mutual information bounds enable linking SBI and BOED.

Optimized design distributions improve inference accuracy.

Real-world applications show notable inference improvements.

Abstract

Simulation-based inference (SBI) is a method to perform inference on a variety of complex scientific models with challenging inference (inverse) problems. Bayesian Optimal Experimental Design (BOED) aims to efficiently use experimental resources to make better inferences. Various stochastic gradient-based BOED methods have been proposed as an alternative to Bayesian optimization and other experimental design heuristics to maximize information gain from an experiment. We demonstrate a link via mutual information bounds between SBI and stochastic gradient-based variational inference methods that permits BOED to be used in SBI applications as SBI-BOED. This link allows simultaneous optimization of experimental designs and optimization of amortized inference functions. We evaluate the pitfalls of naive design optimization using this method in a standard SBI task and demonstrate the utility of a well-chosen design distribution in BOED. We compare this approach on SBI-based models in real-world simulators in epidemiology and biology, showing notable improvements in inference.