Fast Bayesian Inference with Batch Bayesian Quadrature via Kernel Recombination

• URL: http://arxiv.org/abs/2206.04734v1
• Date: Thu, 9 Jun 2022 19:14:52 GMT
• Title: Fast Bayesian Inference with Batch Bayesian Quadrature via Kernel Recombination
• Authors: Masaki Adachi, Satoshi Hayakawa, Martin J{\o}rgensen, Harald Oberhauser, Michael A. Osborne
• Abstract summary: We propose a parallelised (batch) Bayesian quadrature (BQ) method that possesses a provably-exponential convergence rate. We find that our approach significantly outperforms the sampling efficiency of both state-of-the-art BQ techniques and Nested Sampling in various real-world datasets.
• Score: 23.6031259333814
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Calculation of Bayesian posteriors and model evidences typically requires numerical integration. Bayesian quadrature (BQ), a surrogate-model-based approach to numerical integration, is capable of superb sample efficiency, but its lack of parallelisation has hindered its practical applications. In this work, we propose a parallelised (batch) BQ method, employing techniques from kernel quadrature, that possesses a provably-exponential convergence rate. Additionally, just as with Nested Sampling, our method permits simultaneous inference of both posteriors and model evidence. Samples from our BQ surrogate model are re-selected to give a sparse set of samples, via a kernel recombination algorithm, requiring negligible additional time to increase the batch size. Empirically, we find that our approach significantly outperforms the sampling efficiency of both state-of-the-art BQ techniques and Nested Sampling in various real-world datasets, including lithium-ion battery analytics.

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