# Kernel Two-Sample Testing via Directional Components Analysis

arXiv: https://arxiv.org/abs/2508.08564 · HTML: https://mlsanity.com/paper/2508.08564/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 26 references that are in the map.
- First posted on arXiv 12 Aug 2025.

## Builds on (most cited first, 3 of 3)

- [A Permutation-free Kernel Two-Sample Test](https://mlsanity.com/paper/2211.14908/) (2022)
- [Boosting the Power of Kernel Two-Sample Tests](https://mlsanity.com/paper/2302.10687/) (2023)
- [Generalized Kernel Two-Sample Tests](https://mlsanity.com/paper/2011.06127/) (2020)

## Abstract (arXiv)

Standard kernel two-sample tests, such as those based on the Maximum Mean Discrepancy (MMD), aggregate squared differences across all directions in a Reproducing Kernel Hilbert Space (RKHS). However, in finite samples, trailing directional components are noisy, which degrades test power. We propose a novel kernel-based test that resolves this by truncating the spectral decomposition of the MMD, retaining only the well-estimated leading eigen-directions. By aggregating these robust components, our method achieves superior power and robustness, particularly in high-dimensional and unbalanced settings. Furthermore, we introduce a computationally efficient parametric bootstrap procedure for approximating critical values, which is theoretically justified and significantly faster than permutation-based alternatives. Extensive simulations and empirical studies demonstrate that our method maintains strict Type I error control while delivering higher power than existing MMD-based tests.