Classification and Bayesian Optimization for Likelihood-Free Inference

TL;DR

This paper introduces a novel approach for likelihood-free inference in complex models by combining classification techniques with Bayesian optimization to efficiently identify parameters that produce simulated data similar to observed data.

Contribution

It presents a new methodology that addresses the challenges of discrepancy measure selection and efficient parameter space exploration in likelihood-free inference.

Findings

Effective classification-based discrepancy measures

Bayesian optimization accelerates parameter identification

Improved accuracy in likelihood-free inference tasks

Abstract

Some statistical models are specified via a data generating process for which the likelihood function cannot be computed in closed form. Standard likelihood-based inference is then not feasible but the model parameters can be inferred by finding the values which yield simulated data that resemble the observed data. This approach faces at least two major difficulties: The first difficulty is the choice of the discrepancy measure which is used to judge whether the simulated data resemble the observed data. The second difficulty is the computationally efficient identification of regions in the parameter space where the discrepancy is low. We give here an introduction to our recent work where we tackle the two difficulties through classification and Bayesian optimization.