Convergence Guarantees for Gaussian Process Means With Misspecified Likelihoods and Smoothness

Wynne, George G; Briol, François‐Xavier

doi:10.48550/arxiv.2001.10818

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Kernel Interpolant Of Quasi-uniformly Sampled Data2

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2020

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“…for some constant C > 0, with an identical result holding for realisations of Q [84,45]. It follows that choosing N (n) ∼ n guarantees that the conditions of Theorem 5 hold in this setting.…”

Section: Kernel Interpolant Of Quasi-uniformly Sampled Datamentioning

confidence: 69%

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A Kernel Two-Sample Test for Functional Data

Wynne,

Duncan

2020

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We propose a nonparametric two-sample test procedure based on Maximum Mean Discrepancy (MMD) for testing the hypothesis that two samples of functions have the same underlying distribution, using a kernel defined on a function space. This construction is motivated by a scaling analysis of the efficiency of MMD-based tests for datasets of increasing dimension. Theoretical properties of kernels on function spaces and their associated MMD are established and employed to ascertain the efficacy of the newly proposed test, as well as to assess the effects of using functional reconstructions based on discretised function samples. The theoretical results are demonstrated over a range of synthetic and real world datasets.

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Section: Kernel Interpolant Of Quasi-uniformly Sampled Datamentioning

confidence: 69%

“…i=1 but now we assume the points are placed quasi-uniformly in the scattered data approximation sense, for example regularly placed grid points, see [84] and [82,Chapter 4] for other method to obtain quasi-uniform points.…”

Section: Kernel Interpolant Of Quasi-uniformly Sampled Datamentioning

confidence: 99%