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Preprints, Working Papers, ... (Preprint) Year : 2022

Maximum Likelihood Learning of Energy-Based Models for Simulation-Based Inference

Pierre Glaser
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Arnaud Doucet
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Arthur Gretton
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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. Our first method, Amortized Unnormalized Neural Likelihood Estimation (AUNLE), introduces a tilting trick during training that allows to significantly lower the computational cost of inference by enabling the use of efficient MCMC techniques. Our second method, Sequential UNLE (SUNLE), employs a robust doubly intractable approach in order to re-use simulation data and improve posterior accuracy on a specific dataset. 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 Cancer Borealis, matching the performance of other synthetic likelihood methods at a fraction of the simulation budget.
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Dates and versions

hal-03869080 , version 1 (24-11-2022)

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Pierre Glaser, Michael Arbel, Arnaud Doucet, Arthur Gretton. Maximum Likelihood Learning of Energy-Based Models for Simulation-Based Inference. 2022. ⟨hal-03869080⟩
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