Likelihood-free inference via classification

TL;DR

This paper introduces a likelihood-free inference method that uses classification accuracy to measure the discrepancy between observed and simulated data, enabling efficient inference for complex generative models.

Contribution

It proposes a novel approach that transforms likelihood-free inference into a classification problem, leveraging classification accuracy as a discrepancy measure.

Findings

The method is validated through theoretical analysis and simulations.

It effectively performs both point estimation and Bayesian inference.

Demonstrated on real epidemiological data for bacterial infections.

Abstract

Increasingly complex generative models are being used across disciplines as they allow for realistic characterization of data, but a common difficulty with them is the prohibitively large computational cost to evaluate the likelihood function and thus to perform likelihood-based statistical inference. A likelihood-free inference framework has emerged where the parameters are identified by finding values that yield simulated data resembling the observed data. While widely applicable, a major difficulty in this framework is how to measure the discrepancy between the simulated and observed data. Transforming the original problem into a problem of classifying the data into simulated versus observed, we find that classification accuracy can be used to assess the discrepancy. The complete arsenal of classification methods becomes thereby available for inference of intractable generative models. We validate our approach using theory and simulations for both point estimation and Bayesian inference, and demonstrate its use on real data by inferring an individual-based epidemiological model for bacterial infections in child care centers.