Kernel Two-Sample Tests for Manifold Data

arXiv:2105.03425v4 Announce Type: replace-cross
Abstract: We present a study of a kernel-based two-sample test statistic related to the Maximum Mean Discrepancy (MMD) in the manifold data setting, assuming that high-dimensional observations are close to a low-dimensional manifold. We characterize the test level and power in relation to the kernel bandwidth, the number of samples, and the intrinsic dimensionality of the manifold. Specifically, when data densities $p$ and $q$ are supported on a $d$-dimensional sub-manifold ${M}$ embedded in an $m$-dimensional space …

abstract arxiv bandwidth cs.lg data kernel low manifold math.st mean power sample samples stat.ml stat.th study test tests type