# A new measure of dependence: Integrated R2

arXiv: https://arxiv.org/abs/2505.18146 · HTML: https://mlsanity.com/paper/2505.18146/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2025.

## Built on by (most cited first, 2 of 2)

- [Top-k Feature Importance Ranking](https://mlsanity.com/paper/2509.15420/) (2025)
- [Kernel Integrated R2: A Measure of Dependence](https://mlsanity.com/paper/2602.22985/) (2026)

## Abstract (arXiv)

We introduce a novel measure of dependence that captures the extent to which a random variable Y is determined by a random vector X. The measure equals zero precisely when Y and X are independent, and it attains one exactly when Y is almost surely a measurable function of X. We further extend this framework to define a measure of conditional dependence between Y and X given Z. We propose a simple and interpretable estimator with computational complexity comparable to classical correlation coefficients, including those of Pearson, Spearman, and Chatterjee. Leveraging this dependence measure, we develop a tuning-free, model-agnostic variable selection procedure and establish its consistency under appropriate sparsity conditions. Extensive experiments on synthetic and real datasets highlight the strong empirical performance of our methodology and demonstrate substantial gains over existing approaches.