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Kernel Two-Sample Tests for Manifold Data
Feb. 27, 2024, 5:44 a.m. | Xiuyuan Cheng, Yao Xie
cs.LG updates on arXiv.org arxiv.org
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
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