Kernel Based Distribution Tests in High and Infinite Dimensions
Statistics Seminar
28th April 2023, 2:00 pm – 3:00 pm
Fry Building, 2.41
Kernel based discrepancies have found considerable success in constructing statistical tests which are now widely used in statistical machine learning. Examples including Maximum Mean Discrepancy, which is used to perform two-sample tests for equality of datasets, and Kernel Stein Discrepancy which enables goodness-of-fit tests of samples against an (unnormalized) probability density. The effectiveness of the associated tests will hinge on the properties of the underlying kernel-based embedding, which will crucially depend on the dimension of the data.
In this talk, I will present some recent results on the asymptotic behaviour of such tests in high dimensions, exploring properties of the statistic distribution under different scalings of dimension d and sample size n. Building on this, I will discuss the fixed n, infinite d limit which is particularly relevant in the context of functional data and present some results on the construction of kernel-based tests in this setting.
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