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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

• Francois-Xavier Briol, Chris J. Oates, Jon Cockayne, Wilson Ye Chen, Mark Girolami
• 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… (More)

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