On the Sampling Problem for Kernel Quadrature

ICML 2017 Francois-Xavier BriolChris J. OatesJon CockayneWilson Ye ChenMark Girolami

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... (read more)

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