# Bias correction for Chatterjee's graph-based correlation coefficient

arXiv: https://arxiv.org/abs/2508.09040 · HTML: https://mlsanity.com/paper/2508.09040/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Aug 2025.

## Built on by (most cited first, 1 of 1)

- [MixCIT: A Kernel Based Local-Polynomial Debiased Test for Conditional Independence on Mixed-Type Data](https://mlsanity.com/paper/2607.12830/) (2026)

## Abstract (arXiv)

Azadkia and Chatterjee (2021) recently introduced a simple nearest neighbor (NN) graph-based correlation coefficient that consistently detects both independence and functional dependence. Specifically, it approximates a measure of dependence that equals 0 if and only if the variables are independent, and 1 if and only if they are functionally dependent. However, this NN estimator includes a bias term that may vanish at a rate slower than root-n, preventing root-n consistency in general. In this article, we (i) analyze this bias term closely and show that it could become asymptotically negligible when the dimension is smaller than four; and (ii) propose a bias-correction procedure for more general settings. In both regimes, we obtain estimators (either the original or the bias-corrected version) that are root-n consistent and asymptotically normal.