# The Hellinger Correlation

arXiv: https://arxiv.org/abs/1810.10276 · HTML: https://mlsanity.com/paper/1810.10276/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Oct 2018.

## Built on by (most cited first, 4 of 4)

- [Parameter identification in linear non-Gaussian causal models under general confounding](https://mlsanity.com/paper/2405.20856/) (2024)
- [BEAUTY Powered BEAST](https://mlsanity.com/paper/2103.00674/) (2021)
- [Learning Linear Gaussian Polytree Models with Interventions](https://mlsanity.com/paper/2311.04636/) (2023)
- [Enhancing Sufficient Dimension Reduction via Hellinger Correlation](https://mlsanity.com/paper/2405.19704/) (2024)

## Abstract (arXiv)

In this paper, the defining properties of a valid measure of the dependence between two random variables are reviewed and complemented with two original ones, shown to be more fundamental than other usual postulates. While other popular choices are proved to violate some of these requirements, a class of dependence measures satisfying all of them is identified. One particular measure, that we call the Hellinger correlation, appears as a natural choice within that class due to both its theoretical and intuitive appeal. A simple and efficient nonparametric estimator for that quantity is proposed. Synthetic and real-data examples finally illustrate the descriptive ability of the measure, which can also be used as test statistic for exact independence testing.