On a rank-based Azadkia-Chatterjee correlation coefficient

TL;DR

This paper enhances the Azadkia-Chatterjee correlation coefficient by incorporating a rank-based nearest neighbor graph to achieve scale invariance, providing theoretical guarantees for this new approach.

Contribution

It introduces a rank-based NNG for the Azadkia-Chatterjee coefficient, ensuring scale invariance and establishing its theoretical properties.

Findings

The rank-based NNG improves scale invariance of the correlation coefficient.

Theoretical guarantees for the rank-based Azadkia-Chatterjee coefficient are provided.

The method maintains strong correlation detection capabilities.

Abstract

Azadkia and Chatterjee (Azadkia and Chatterjee, 2021) recently introduced a graph-based correlation coefficient that has garnered significant attention. The method relies on a nearest neighbor graph (NNG) constructed from the data. While appealing in many respects, NNGs typically lack the desirable property of scale invariance; that is, changing the scales of certain covariates can alter the structure of the graph. This paper addresses this limitation by employing a rank-based NNG proposed by Rosenbaum (2005) and gives necessary theoretical guarantees for the corresponding rank-based Azadkia-Chatterjee correlation coefficient.