Fast Bayesian Inference with Batch Bayesian Quadrature via Kernel Recombination
This work addresses the practical limitation of slow, non-parallel BQ for researchers and practitioners needing efficient Bayesian inference, offering a significant improvement but being incremental as it builds on existing BQ and kernel quadrature methods.
The paper tackles the lack of parallelization in Bayesian quadrature (BQ) for numerical integration in Bayesian inference by proposing a batch BQ method using kernel recombination, achieving an empirically exponential convergence rate and outperforming state-of-the-art BQ techniques and Nested Sampling in efficiency on real-world datasets like lithium-ion battery analytics.
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.