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Poster
Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with Theoretical Guarantees
François-Xavier Briol · Chris Oates · Mark Girolami · Michael A Osborne

Tue Dec 08 04:00 PM -- 08:59 PM (PST) @ 210 C #57
in Poster Session »

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). Under FWBQ, convergence to the true value of the integral is shown to be exponential and posterior contraction rates are proven to be superexponential. In simulations, FWBQ is competitive with state-of-the-art methods and out-performs alternatives based on Frank-Wolfe optimisation. Our approach is applied to successfully quantify numerical error in the solution to a challenging model choice problem in cellular biology.

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Author Information

François-Xavier Briol (University of Warwick)
Chris Oates (University of Tech., Sydney)
Mark Girolami (University of Warwick, The Alan Turing Institute for Data Science)
Michael A Osborne (U Oxford)

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