On the use of random forest for two-sample testing

We follow the line of using classifiers for two-sample testing and propose several tests based on the Random Forest classifier. The developed tests are easy to use, require no tuning and are applicable for any distribution on $\mathbb{R}^p$, even in high-dimensions. We provide a comprehensive treatment for the use of classification for two-sample testing, derive the distribution of our tests under the Null and provide a power analysis, both in theory and with simulations. To simplify the use of the method, we also provide the R-package "hypoRF".