Invariant Priors for Bayesian Quadrature
This work addresses a domain-specific problem in numerical integration for researchers, but it is incremental as it builds on existing Bayesian quadrature methods.
The paper tackled the problem of improving sample efficiency in Bayesian quadrature by developing priors that encode invariance under unitary transformations like rotations and flips, achieving superior performance over standard methods on synthetic and real-world applications.
Bayesian quadrature (BQ) is a model-based numerical integration method that is able to increase sample efficiency by encoding and leveraging known structure of the integration task at hand. In this paper, we explore priors that encode invariance of the integrand under a set of bijective transformations in the input domain, in particular some unitary transformations, such as rotations, axis-flips, or point symmetries. We show initial results on superior performance in comparison to standard Bayesian quadrature on several synthetic and one real world application.