# Testing Hypotheses by Regularized Maximum Mean Discrepancy

arXiv: https://arxiv.org/abs/1305.0423 · HTML: https://mlsanity.com/paper/1305.0423/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 May 2013.

## Built on by (most cited first, 3 of 3)

- [The "Beatrix'' Resurrections: Robust Backdoor Detection via Gram Matrices](https://mlsanity.com/paper/2209.11715/) (2022)
- [RAI4IoE: Responsible AI for Enabling the Internet of Energy](https://mlsanity.com/paper/2309.11691/) (2023)
- [Variance Matters: Improving Domain Adaptation via Stratified Sampling](https://mlsanity.com/paper/2512.05226/) (2025)

## Abstract (arXiv)

Do two data samples come from different distributions? Recent studies of this fundamental problem focused on embedding probability distributions into sufficiently rich characteristic Reproducing Kernel Hilbert Spaces (RKHSs), to compare distributions by the distance between their embeddings. We show that Regularized Maximum Mean Discrepancy (RMMD), our novel measure for kernel-based hypothesis testing, yields substantial improvements even when sample sizes are small, and excels at hypothesis tests involving multiple comparisons with power control. We derive asymptotic distributions under the null and alternative hypotheses, and assess power control. Outstanding results are obtained on: challenging EEG data, MNIST, the Berkley Covertype, and the Flare-Solar dataset.