MMD Aggregated Two-Sample Test. (arXiv:2110.15073v2 [stat.ML] UPDATED)

Web: http://arxiv.org/abs/2110.15073

We propose a novel nonparametric two-sample test based on the Maximum Mean
Discrepancy (MMD), which is constructed by aggregating tests with different
kernel bandwidths. This aggregation procedure, called MMDAgg, ensures that test
power is maximised over the collection of kernels used, without requiring
held-out data for kernel selection (which results in a loss of test power), or
arbitrary kernel choices such as the median heuristic. We work in the
non-asymptotic framework, and prove that our aggregated test is minimax
adaptive …

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