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.
翻译:贝叶西亚后方和模型证据的计算通常需要数字集成。贝叶斯二次曲线(BQ)是一种以代位模型为基础的数字集成方法,它能够产生超级样本效率,但缺乏平行性妨碍了其实际应用。在这项工作中,我们建议采用平行(批量)的BQ方法,使用内核二次曲线的技术,这种技术具有可辨别和可辨别的耗尽的趋同率。此外,正如内斯泰德取样一样,我们的方法允许同时推断后方和模型证据。我们BQ代位模型的样本通过内核再组合算法重新选择,给一组稀有的样本,需要极少的额外时间来增加批量尺寸。我们发现,我们的方法大大超出了包括锂电池分析器在内的各种真实世界数据集中最先进的BQ技术和内层取样效率。