# On boosting the power of Chatterjee's rank correlation

arXiv: https://arxiv.org/abs/2108.06828 · HTML: https://mlsanity.com/paper/2108.06828/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Aug 2021.

## Built on by (most cited first, 10 of 10)

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- [Limit theorems of Chatterjee's rank correlation](https://mlsanity.com/paper/2204.08031/) (2022)
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- [Vine Copulas as Differentiable Computational Graphs](https://mlsanity.com/paper/2506.13318/) (2025)
- [XicorAttention: Time Series Transformer Using Attention with Nonlinear Correlation](https://mlsanity.com/paper/2506.02694/) (2025)
- [Kernel Integrated R2: A Measure of Dependence](https://mlsanity.com/paper/2602.22985/) (2026)
- [Causality-Encoded Diffusion Models for Interventional Sampling and Edge Inference](https://mlsanity.com/paper/2604.21843/) (2026)
- [Nearest-Neighbor Radii under Dependent Sampling](https://mlsanity.com/paper/2605.14343/) (2026)

## Abstract (arXiv)

Chatterjee (2021)'s ingenious approach to estimating a measure of dependence first proposed by Dette et al. (2013) based on simple rank statistics has quickly caught attention. This measure of dependence has the unusual property of being between 0 and 1, and being 0 or 1 if and only if the corresponding pair of random variables is independent or one is a measurable function of the other almost surely. However, more recent studies (Cao and Bickel, 2020; Shi et al., 2021b) showed that independence tests based on Chatterjee's rank correlation are unfortunately rate-inefficient against various local alternatives and they call for variants. We answer this call by proposing revised Chatterjee's rank correlations that still consistently estimate the same dependence measure but provably achieve near-parametric efficiency in testing against Gaussian rotation alternatives. This is possible via incorporating many right nearest neighbors in constructing the correlation coefficients. We thus overcome the "only one disadvantage" of Chatterjee's rank correlation (Chatterjee, 2021, Section 7).