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Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with Theoretical Guarantees

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Title: Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with Theoretical Guarantees
Authors: Briol, F-X
Oates, CJ
Girolami, M
Osborne, MA
Item Type: Conference Paper
Abstract: 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.
Issue Date: 1-Jan-2015
Date of Acceptance: 1-Sep-2015
URI: http://hdl.handle.net/10044/1/53208
Start Page: 1162
End Page: 1170
Copyright Statement: © The Authors
Conference Name: Neural Information Processing Systems (NIPS)
Keywords: stat.ML
1701 Psychology
1702 Cognitive Science
Appears in Collections:Mathematics
Faculty of Natural Sciences