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Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with Theoretical Guarantees

• François-Xavier Briol, Chris J. Oates, Mark A. Girolami, Michael A. Osborne
• NIPS
• 2015

There is renewed interest in formulating integration as a statistical 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… (More)

Probabilistic Integration

• François-Xavier Briol, Chris J. Oates, Mark A. Girolami, Michael A. Osborne, Dino Sejdinovic
• ArXiv
• 2015

On the Sampling Problem for Kernel Quadrature

• François-Xavier Briol, Chris J. Oates, Jon Cockayne, Wilson Ye Chen, Mark A. Girolami
• ICML
• 2017

The standard Kernel Quadrature method for numerical integration with random point sets (also called Bayesian Monte Carlo) is known to converge in root mean square error at a rate determined by the ratio s/d, where s and d encode the smoothness and dimension of the integrand. However, an empirical investigation reveals that the rate constant C is highly… (More)

Geometry and Dynamics for Markov Chain Monte Carlo

• Alessandro Barp, François-Xavier Briol, Anthony D. Kennedy, Mark A. Girolami
• ArXiv
• 2017

Markov Chain Monte Carlo methods have revolutionised mathematical computation and enabled statistical inference within many previously intractable models. In this context, Hamiltonian dynamics have been proposed as an efficient way of building chains which can explore probability densities efficiently. The method emerges from physics and geometry and these… (More)

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