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Preprints, Working Papers, ... Year : 2024

Bayesian Likelihood Free Inference using Mixtures of Experts

Abstract

We extend Bayesian Synthetic Likelihood (BSL) methods to non-Gaussian approximations of the likelihood function. In this setting, we introduce Mixtures of Experts (MoEs), a class of neural network models, as surrogate likelihoods that exhibit desirable approximation theoretic properties. Moreover, MoEs can be estimated using Expectation-Maximization algorithm-based approaches, such as the Gaussian Locally Linear Mapping model estimators that we implement. Further, we provide theoretical evidence towards the ability of our procedure to estimate and approximate a wide range of likelihood functions. Through simulations, we demonstrate the superiority of our approach over existing BSL variants in terms of both posterior approximation accuracy and computational efficiency.
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Dates and versions

hal-04436187 , version 1 (03-02-2024)

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  • HAL Id : hal-04436187 , version 1

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Florence Forbes, Hien Duy Nguyen, Trungtin Nguyen. Bayesian Likelihood Free Inference using Mixtures of Experts. 2024. ⟨hal-04436187⟩
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