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Frank-Wolfe Bayesian quadrature: Probabilistic integration with theoretical guarantees

Briol, FX; Oates, CJ; Girolami, M; Osborne, MA; (2015) Frank-Wolfe Bayesian quadrature: Probabilistic integration with theoretical guarantees. In: Advances in Neural Information Processing Systems 28 (NIPS 2015). Neural Information Processing Systems (NIPS) Green open access

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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.

Type: Proceedings paper
Title: Frank-Wolfe Bayesian quadrature: Probabilistic integration with theoretical guarantees
Event: Neural Information Processing Systems 2015
Open access status: An open access version is available from UCL Discovery
Publisher version: https://papers.nips.cc/paper/5749-frank-wolfe-baye...
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/10079229
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