# Generalized Kernel Two-Sample Tests

arXiv: https://arxiv.org/abs/2011.06127 · HTML: https://mlsanity.com/paper/2011.06127/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Nov 2020.

## Built on by (most cited first, 5 of 5)

- [Boosting the Power of Kernel Two-Sample Tests](https://mlsanity.com/paper/2302.10687/) (2023)
- [A fast and effective kernel two-sample test for large-scale data](https://mlsanity.com/paper/2110.03118/) (2021)
- [Kernel Two-Sample Testing via Directional Components Analysis](https://mlsanity.com/paper/2508.08564/) (2025)
- [A nonparametric two-sample test using a parametric integral probability metric](https://mlsanity.com/paper/2606.16941/) (2026)
- [What FID Hides: Detecting, Ranking, and Diagnosing Deviations in Generative Evaluation](https://mlsanity.com/paper/2608.24881/) (2026)

## Abstract (arXiv)

Kernel two-sample tests have been widely used for multivariate data to test equality of distributions. However, existing tests based on mapping distributions into a reproducing kernel Hilbert space mainly target specific alternatives and do not work well for some scenarios when the dimension of the data is moderate to high due to the curse of dimensionality. We propose a new test statistic that makes use of a common pattern under moderate and high dimensions and achieves substantial power improvements over existing kernel two-sample tests for a wide range of alternatives. We also propose alternative testing procedures that maintain high power with low computational cost, offering easy off-the-shelf tools for large datasets. The new approaches are compared to other state-of-the-art tests under various settings and show good performance. We showcase the new approaches through two applications: The comparison of musks and non-musks using the shape of molecules, and the comparison of taxi trips starting from John F. Kennedy airport in consecutive months. All proposed methods are implemented in an R package kerTests.