Optimizing Likelihoods via Mutual Information: Bridging Simulation-Based Inference and Bayesian Optimal Experimental Design
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| Format: | Preprint |
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2025
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| _version_ | 1866909488553918464 |
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| author | Zaballa, Vincent D. Hui, Elliot E. |
| author_facet | Zaballa, Vincent D. Hui, Elliot E. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08004 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimizing Likelihoods via Mutual Information: Bridging Simulation-Based Inference and Bayesian Optimal Experimental Design Zaballa, Vincent D. Hui, Elliot E. Machine Learning 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. |
| title | Optimizing Likelihoods via Mutual Information: Bridging Simulation-Based Inference and Bayesian Optimal Experimental Design |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2502.08004 |