Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Models

TL;DR

This paper introduces a Bayesian optimization approach to likelihood-free inference for complex simulator-based models, significantly reducing the computational cost by minimizing the number of simulations needed.

Contribution

It presents a novel method combining probabilistic discrepancy modeling with Bayesian optimization to improve efficiency in likelihood-free inference for general generative models.

Findings

Reduces simulation requirements by several orders of magnitude

Accelerates inference process significantly

Applicable to complex, noisy dynamical systems

Abstract

Our paper deals with inferring simulator-based statistical models given some observed data. A simulator-based model is a parametrized mechanism which specifies how data are generated. It is thus also referred to as generative model. We assume that only a finite number of parameters are of interest and allow the generative process to be very general; it may be a noisy nonlinear dynamical system with an unrestricted number of hidden variables. This weak assumption is useful for devising realistic models but it renders statistical inference very difficult. The main challenge is the intractability of the likelihood function. Several likelihood-free inference methods have been proposed which share the basic idea of identifying the parameters by finding values for which the discrepancy between simulated and observed data is small. A major obstacle to using these methods is their computational cost. The cost is largely due to the need to repeatedly simulate data sets and the lack of knowledge about how the parameters affect the discrepancy. We propose a strategy which combines probabilistic modeling of the discrepancy with optimization to facilitate likelihood-free inference. The strategy is implemented using Bayesian optimization and is shown to accelerate the inference through a reduction in the number of required simulations by several orders of magnitude.