Boosting the Power of Kernel Two-Sample Tests

Understand

The kernel two-sample test based on the maximum mean discrepancy (MMD) is one of the most popular methods for detecting differences between two distributions over general metric spaces.

• In this paper we propose a method to boost the power of the kernel test by combining MMD estimates over multiple kernels using their Mahalanobis distance.
• We derive the asymptotic null distribution of the proposed test statistic and use a multiplier bootstrap approach to efficiently compute the rejection region.
• The resulting test is universally consistent and, since it is obtained by aggregating over a collection of kernels/bandwidths, is more powerful in detecting a wide range of alternatives in finite samples.