Fast bayesian inference with batch bayesian quadrature via kernel recombination

Conference item

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 an empirically 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.

Authors: Adachi, M; Hayakawa, S; Jorgensen, M; Oberhauser, H; Osborne, MA

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: NeurIPS Proceedings
• Host title: Proceedings of the 36th Conference on Neural Information Processing Systems (NeurIPS 2022)
• Publication date: 2022-12-09
• Acceptance date: 2022-09-15
• Event title: 36th Conference on Neural Information Processing Systems (NeurIPS 2022)
• Event location: New Orleans, LA, USA
• Event website: https://nips.cc/
• Event start date: 2022-11-28
• Event end date: 2022-12-09
• Language: English
• Keywords: FFR