Two-sample test with kernel methods.

A classic problem in statistics is to test whether two populations of observations are similar (i.e. equally distributed). The first tests developed were parametric, it means that we had to make strong assumptions on the underlying distribution, typically Gaussian assumptions. They were also not well-defined for high-dimension (when the number of features exceeds the number of observations). Recently, non-parametric two-sample tests especially designed for high-dimension were developed. I will present a group of such tests very popular in the machine learning community, which takes roots in kernel methods, a branch of non-linear statistics