Citation

BibTex format

@inproceedings{Briol,
author = {Briol, F-X and Oates, CJ and Cockayne, J and Chen, WY and Girolami, M},
pages = {586--595},
publisher = {PMLR},
title = {On the Sampling Problem for Kernel Quadrature},
url = {http://arxiv.org/abs/1706.03369v1},
}

RIS format (EndNote, RefMan)

TY  - CPAPER
AB - 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 sensitive to the distribution of the random points. In contrast to standard Monte Carlo integration, for which optimal importance sampling is well-understood, the sampling distribution that minimises $C$ for Kernel Quadrature does not admit a closed form. This paper argues that the practical choice of sampling distribution is an important open problem. One solution is considered; a novel automatic approach based on adaptive tempering and sequential Monte Carlo.Empirical results demonstrate a dramatic reduction in integration error of up to 4 orders of magnitude can be achieved with the proposed method.
AU - Briol,F-X
AU - Oates,CJ
AU - Cockayne,J
AU - Chen,WY
AU - Girolami,M
EP - 595
PB - PMLR
SP - 586
TI - On the Sampling Problem for Kernel Quadrature
UR - http://arxiv.org/abs/1706.03369v1
UR - http://proceedings.mlr.press/v70/briol17a.html
UR - http://hdl.handle.net/10044/1/53203
ER -