Bayesian Quadrature

Bayesian quadrature (BQ) is a probabilistic numerical method for efficiently estimating integrals, particularly valuable when evaluating the integrand is computationally expensive. Current research focuses on improving BQ's scalability and accuracy through techniques like Bayesian neural networks and sparse Gaussian processes, as well as adapting it for parallel computation and diverse problem settings including Bayesian optimization and reinforcement learning. These advancements enhance BQ's applicability across various fields, from accelerating large language model inference and Bayesian model selection to optimizing complex control systems and improving Bayesian inference in computationally demanding applications.