Automated Model Selection with Bayesian Quadrature
This work addresses the challenge of reliable model comparison in machine learning, particularly for expensive models, though it is incremental as it builds on prior Bayesian quadrature techniques.
The paper tackles the problem of inefficient model selection for computationally expensive models by proposing an automated Bayesian quadrature algorithm that maximizes mutual information to compute model posterior probabilities, achieving more accurate estimates with fewer likelihood evaluations than existing methods.
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.