Maximum Likelihood Learning of Unnormalized Models for Simulation-Based Inference

• URL: http://arxiv.org/abs/2210.14756v2
• Date: Tue, 18 Apr 2023 09:45:23 GMT
• Title: Maximum Likelihood Learning of Unnormalized Models for Simulation-Based Inference
• Authors: Pierre Glaser, Michael Arbel, Samo Hromadka, Arnaud Doucet, Arthur Gretton
• Abstract summary: We introduce two synthetic likelihood methods for Simulation-Based Inference. We learn a conditional energy-based model (EBM) of the likelihood using synthetic data generated by the simulator. We demonstrate the properties of both methods on a range of synthetic datasets, and apply them to a model of the neuroscience network in the crab.
• Score: 44.281860162298564
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce two synthetic likelihood methods for Simulation-Based Inference (SBI), to conduct either amortized or targeted inference from experimental observations when a high-fidelity simulator is available. Both methods learn a conditional energy-based model (EBM) of the likelihood using synthetic data generated by the simulator, conditioned on parameters drawn from a proposal distribution. The learned likelihood can then be combined with any prior to obtain a posterior estimate, from which samples can be drawn using MCMC. Our methods uniquely combine a flexible Energy-Based Model and the minimization of a KL loss: this is in contrast to other synthetic likelihood methods, which either rely on normalizing flows, or minimize score-based objectives; choices that come with known pitfalls. We demonstrate the properties of both methods on a range of synthetic datasets, and apply them to a neuroscience model of the pyloric network in the crab, where our method outperforms prior art for a fraction of the simulation budget.

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