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

• URL: http://arxiv.org/abs/2502.08004v1
• Date: Tue, 11 Feb 2025 22:58:18 GMT
• Title: Optimizing Likelihoods via Mutual Information: Bridging Simulation-Based Inference and Bayesian Optimal Experimental Design
• Authors: Vincent D. Zaballa, Elliot E. Hui,
• Abstract summary: gradient-based BOED methods have been proposed as an alternative to Bayesian optimization and other experimental designs. We show a link via mutual information bounds between SBI and gradient-based variational inference methods that permits BOED to be used in SBI applications as SBI-BOED. We compare this approach on SBI-based models in real-world simulators in epidemiology and biology, showing notable improvements in inference.
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• 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.

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