Adaptive Two-Sample Testing Using Graph-Based Methods

Music City Center 

The two-sample test is a fundamental problem in statistics with a wide range of applications. In high-dimensional settings, graph-based methods have gained considerable attention for their flexibility and minimal distributional assumptions. However, their performance is highly sensitive to tuning parameters, such as the choice of k and the norm used in k-MST construction. To address this challenge, we propose a novel data-driven approach that adaptively selects both k and the appropriate norm, enabling the test statistic to construct similarity graphs that more effectively capture distributional differences. Our method consistently outperforms existing graph-based tests with recommended parameter choices and other adaptive methods across a broad range of scenarios.

High dimensional statistics

Graph-based method

Adaptive method 

Section on Nonparametric Statistics