# On Ranking-based Tests of Independence

arXiv: https://arxiv.org/abs/2403.07464 · HTML: https://mlsanity.com/paper/2403.07464/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 75 references that are in the map.
- First posted on arXiv 12 Mar 2024.

## Builds on (most cited first, 10 of 10)

- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [Turning the Tables: Biased, Imbalanced, Dynamic Tabular Datasets for ML Evaluation](https://mlsanity.com/paper/2211.13358/) (2022)
- [Multivariate Rank-based Distribution-free Nonparametric Testing using Measure Transportation](https://mlsanity.com/paper/1909.08733/) (2019)
- [A Witness Two-Sample Test](https://mlsanity.com/paper/2102.05573/) (2021)
- [Nonparametric independence testing via mutual information](https://mlsanity.com/paper/1711.06642/) (2017)
- [Measuring dependence powerfully and equitably](https://mlsanity.com/paper/1505.02213/) (2015)
- [Consistent distribution-free K-sample and independence tests for univariate random variables](https://mlsanity.com/paper/1410.6758/) (2014)
- [A High-dimensional Convergence Theorem for U-statistics with Applications to Kernel-based Testing](https://mlsanity.com/paper/2302.05686/) (2023)
- [Concentration Inequalities for Two-Sample Rank Processes with Application to Bipartite Ranking](https://mlsanity.com/paper/2104.02943/) (2021)
- [Data-Driven Representations for Testing Independence: Modeling, Analysis and Connection with Mutual Information Estimation](https://mlsanity.com/paper/2110.14122/) (2021)

## Abstract (arXiv)

In this paper we develop a novel nonparametric framework to test the independence of two random variables X and Y with unknown respective marginals H(dx) and G(dy) and joint distribution F(dx dy), based on it Receiver Operating Characteristic (ROC) analysis and bipartite ranking. The rationale behind our approach relies on the fact that, the independence hypothesis H0 is necessarily false as soon as the optimal scoring function related to the pair of distributions (Hotimes G,; F), obtained from a bipartite ranking algorithm, has a ROC curve that deviates from the main diagonal of the unit square.We consider a wide class of rank statistics encompassing many ways of deviating from the diagonal in the ROC space to build tests of independence. Beyond its great flexibility, this new method has theoretical properties that far surpass those of its competitors. Nonasymptotic bounds for the two types of testing errors are established. From an empirical perspective, the novel procedure we promote in this paper exhibits a remarkable ability to detect small departures, of various types, from the null assumption H0, even in high dimension, as supported by the numerical experiments presented here.