Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with Theoretical Guarantees

Understand

There is renewed interest in formulating integration as an inference problem, motivated by obtaining a full distribution over numerical error that can be propagated through subsequent computation.

• Current methods, such as Bayesian Quadrature, demonstrate impressive empirical performance but lack theoretical analysis.
• An important challenge is to reconcile these probabilistic integrators with rigorous convergence guarantees.
• In this paper, we present the first probabilistic integrator that admits such theoretical treatment, called Frank-Wolfe Bayesian Quadrature (FWBQ).