Optimal Prediction-Augmented Algorithms for Testing Independence of Distributions

• URL: http://arxiv.org/abs/2603.04635v1
• Date: Wed, 04 Mar 2026 21:55:08 GMT
• Title: Optimal Prediction-Augmented Algorithms for Testing Independence of Distributions
• Authors: Maryam Aliakbarpour, Alireza Azizi, Ria Stevens,
• Abstract summary: We address the problem of testing the independence of $p$ over multiple random variables.<n>We design testers that incorporate auxiliary, but potentially untrustworthy, predictive information.<n>Our framework ensures that the tester remains robust, maintaining worst-case validity regardless of the prediction's quality.
• Score: 4.200594864147057
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Independence testing is a fundamental problem in statistical inference: given samples from a joint distribution $p$ over multiple random variables, the goal is to determine whether $p$ is a product distribution or is $ε$-far from all product distributions in total variation distance. In the non-parametric finite-sample regime, this task is notoriously expensive, as the minimax sample complexity scales polynomially with the support size. In this work, we move beyond these worst-case limitations by leveraging the framework of \textit{augmented distribution testing}. We design independence testers that incorporate auxiliary, but potentially untrustworthy, predictive information. Our framework ensures that the tester remains robust, maintaining worst-case validity regardless of the prediction's quality, while significantly improving sample efficiency when the prediction is accurate. Our main contributions include: (i) a bivariate independence tester for discrete distributions that adaptively reduces sample complexity based on the prediction error; (ii) a generalization to the high-dimensional multivariate setting for testing the independence of $d$ random variables; and (iii) matching minimax lower bounds demonstrating that our testers achieve optimal sample complexity.

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