{
  "id": "2502.08004",
  "version": "v1",
  "published": "2025-02-11T22:58:18.000Z",
  "updated": "2025-02-11T22:58:18.000Z",
  "title": "Optimizing Likelihoods via Mutual Information: Bridging Simulation-Based Inference and Bayesian Optimal Experimental Design",
  "authors": [
    "Vincent D. Zaballa",
    "Elliot E. Hui"
  ],
  "comment": "Preprint. Under Review",
  "categories": [
    "stat.ML",
    "cs.LG"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-11T22:58:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bayesian optimal experimental design",
      "mutual information",
      "bridging simulation-based inference",
      "gradient-based variational inference methods",
      "optimizing likelihoods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}