# Automated Model Selection with Bayesian Quadrature

arXiv: https://arxiv.org/abs/1902.09724 · HTML: https://mlsanity.com/paper/1902.09724/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Feb 2019.

## Built on by (most cited first, 5 of 5)

- [Active Testing: Sample-Efficient Model Evaluation](https://mlsanity.com/paper/2103.05331/) (2021)
- [Fast Bayesian Inference with Batch Bayesian Quadrature via Kernel Recombination](https://mlsanity.com/paper/2206.04734/) (2022)
- [Marginalising over Stationary Kernels with Bayesian Quadrature](https://mlsanity.com/paper/2106.07452/) (2021)
- [Model Selection for Production System via Automated Online Experiments](https://mlsanity.com/paper/2105.13420/) (2021)
- [Bayesian Quadrature](https://mlsanity.com/paper/2602.16218/) (2026)

## Abstract (arXiv)

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.