# Bayesian Kernel Two-Sample Testing

arXiv: https://arxiv.org/abs/2002.05550 · HTML: https://mlsanity.com/paper/2002.05550/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2020.

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

- [An Overview of Causal Inference using Kernel Embeddings](https://mlsanity.com/paper/2410.22754/) (2024)
- [A Scalable Nystrom-Based Kernel Two-Sample Test with Permutations](https://mlsanity.com/paper/2502.13570/) (2025)
- [Bayesian Counterfactual Mean Embeddings and Off-Policy Evaluation](https://mlsanity.com/paper/2211.01518/) (2022)

## Abstract (arXiv)

In modern data analysis, nonparametric measures of discrepancies between random variables are particularly important. The subject is well-studied in the frequentist literature, while the development in the Bayesian setting is limited where applications are often restricted to univariate cases. Here, we propose a Bayesian kernel two-sample testing procedure based on modelling the difference between kernel mean embeddings in the reproducing kernel Hilbert space utilising the framework established by Flaxman et al (2016). The use of kernel methods enables its application to random variables in generic domains beyond the multivariate Euclidean spaces. The proposed procedure results in a posterior inference scheme that allows an automatic selection of the kernel parameters relevant to the problem at hand. In a series of synthetic experiments and two real data experiments (i.e. testing network heterogeneity from high-dimensional data and six-membered monocyclic ring conformation comparison), we illustrate the advantages of our approach.