Comparing distributions: $\ell_1$ geometry improves kernel two-sample testing

Are two sets of observations drawn from the same distribution? This problem is a two-sample test. Kernel methods lead to many appealing properties. Indeed state-of-the-art approaches use the L^2distance between kernel-based distribution representatives to derive their test statistics. Here, we show that L^pdistances (with p\geq 1 between these distribution representatives give metrics on the space of distributions that are well-behaved...