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- W4297788920 abstract "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." @default.
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- W4297788920 date "2017-06-11" @default.
- W4297788920 modified "2023-10-14" @default.
- W4297788920 title "On the Sampling Problem for Kernel Quadrature" @default.
- W4297788920 doi "https://doi.org/10.48550/arxiv.1706.03369" @default.
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