Automated Model Selection with Bayesian Quadrature

TL;DR

This paper introduces an automated Bayesian quadrature-based method for efficient model selection, significantly reducing the number of likelihood evaluations needed to accurately estimate model posterior probabilities.

Contribution

It develops a novel algorithm that maximizes mutual information for better sample efficiency in model comparison, improving over existing Monte Carlo and BQ methods.

Findings

More accurate model posterior estimates with fewer likelihood evaluations

Outperforms standard Bayesian quadrature and Monte Carlo in synthetic and real-world tests

Efficiently compares multiple models with limited likelihood data

Abstract

We present a novel technique for tailoring Bayesian quadrature (BQ) to model selection. The state-of-the-art for comparing the evidence of multiple models relies on Monte Carlo methods, which converge slowly and are unreliable for computationally expensive models. Previous research has shown that BQ offers sample efficiency superior to Monte Carlo in computing the evidence of an individual model. However, applying BQ directly to model comparison may waste computation producing an overly-accurate estimate for the evidence of a clearly poor model. We propose an automated and efficient algorithm for computing the most-relevant quantity for model selection: the posterior probability of a model. Our technique maximizes the mutual information between this quantity and observations of the models' likelihoods, yielding efficient acquisition of samples across disparate model spaces when likelihood observations are limited. Our method produces more-accurate model posterior estimates using fewer model likelihood evaluations than standard Bayesian quadrature and Monte Carlo estimators, as we demonstrate on synthetic and real-world examples.