A Fast and Effective Large-Scale Two-Sample Test Based on Kernels

Abstract: Kernel two-sample tests have been widely used and the development of efficient methods for high-dimensional large-scale data is gaining more and more attention as we are entering the big data era. However, existing methods, such as the maximum mean discrepancy (MMD) and recently proposed kernel-based tests for large-scale data, are computationally intensive to implement and/or ineffective for some common alternatives for high-dimensional data. In this paper, we propose a new test that exhibits high power for a wide range of alternatives. Moreover, the new test is more robust to high dimensions than existing methods and does not require optimization procedures for the choice of kernel bandwidth and other parameters by data splitting. Numerical studies show that the new approach performs well in both synthetic and real world data.