Kernel Two-Sample Testing via Directional Components Analysis

TL;DR

This paper introduces a new kernel-based two-sample test that improves detection power and robustness by focusing on well-estimated spectral components in RKHS, especially in high-dimensional settings.

Contribution

It develops a spectral decomposition approach for MMD, emphasizing reliable eigen-directions, and combines multiple kernels for enhanced test performance.

Findings

Higher test power in high-dimensional data

Maintains nominal Type I error rate

Faster than permutation-based methods

Abstract

We propose a novel kernel-based two-sample test that leverages the spectral decomposition of the maximum mean discrepancy (MMD) statistic to identify and utilize well-estimated directional components in reproducing kernel Hilbert space (RKHS). Our approach is motivated by the observation that the estimation quality of these components varies significantly, with leading eigen-directions being more reliably estimated in finite samples. By focusing on these directions and aggregating information across multiple kernels, the proposed test achieves higher power and improved robustness, especially in high-dimensional and unbalanced sample settings. We further develop a computationally efficient multiplier bootstrap procedure for approximating critical values, which is theoretically justified and significantly faster than permutation-based alternatives. Extensive simulations and empirical studies on microarray datasets demonstrate that our method maintains the nominal Type I error rate and delivers superior power compared to other existing MMD-based tests.