# Universally Consistent K-Sample Tests via Dependence Measures

arXiv: https://arxiv.org/abs/1910.08883 · HTML: https://mlsanity.com/paper/1910.08883/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Oct 2019.

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

- [Detecting Perspective Shifts in Multi-agent Systems](https://mlsanity.com/paper/2512.05013/) (2025)
- [Private measurement of nonlinear correlations between data hosted across multiple parties](https://mlsanity.com/paper/2110.09670/) (2021)
- [Explaining Categorical Feature Interactions Using Graph Covariance and LLMs](https://mlsanity.com/paper/2501.14932/) (2025)

## Abstract (arXiv)

The K-sample testing problem involves determining whether K groups of data points are each drawn from the same distribution. Analysis of variance is arguably the most classical method to test mean differences, along with several recent methods to test distributional differences. In this paper, we demonstrate the existence of a transformation that allows K-sample testing to be carried out using any dependence measure. Consequently, universally consistent K-sample testing can be achieved using a universally consistent dependence measure, such as distance correlation and the Hilbert-Schmidt independence criterion. This enables a wide range of dependence measures to be easily applied to K-sample testing.