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Related papers: Minimax Optimal Conditional Independence Testing

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Conditional independence (CI) testing is a fundamental task in modern statistics and machine learning. The conditional randomization test (CRT) was recently introduced to test whether two random variables, $X$ and $Y$, are conditionally…

Machine Learning · Statistics 2024-12-19 Yanfeng Yang , Shuai Li , Yingjie Zhang , Zhuoran Sun , Hai Shu , Ziqi Chen , Renming Zhang

We investigate the sample complexity of mutual information and conditional mutual information testing. For conditional mutual information testing, given access to independent samples of a triple of random variables $(A, B, C)$ with unknown…

Data Structures and Algorithms · Computer Science 2025-06-05 Jan Seyfried , Sayantan Sen , Marco Tomamichel

Conditional independence (CI) testing arises naturally in many scientific problems and applications domains. The goal of this problem is to investigate the conditional independence between a response variable $Y$ and another variable $X$,…

Methodology · Statistics 2025-10-07 Adel Javanmard , Mohammad Mehrabi

For a continuous random variable $Z$, testing conditional independence $X \perp\!\!\!\perp Y |Z$ is known to be a particularly hard problem. It constitutes a key ingredient of many constraint-based causal discovery algorithms. These…

Statistics Theory · Mathematics 2021-12-21 Philip A. Boeken , Joris M. Mooij

We present and evaluate the Fast (conditional) Independence Test (FIT) -- a nonparametric conditional independence test. The test is based on the idea that when $P(X \mid Y, Z) = P(X \mid Y)$, $Z$ is not useful as a feature to predict $X$,…

Machine Learning · Statistics 2018-04-10 Krzysztof Chalupka , Pietro Perona , Frederick Eberhardt

This article addresses the problem of testing the conditional independence of two generic random vectors $X$ and $Y$ given a third random vector $Z$, which plays an important role in statistical and machine learning applications. We propose…

Methodology · Statistics 2024-07-26 Yi Zhang , Linjun Huang , Yun Yang , Xiaofeng Shao

In this paper we introduce a new measure of conditional dependence between two random vectors ${\boldsymbol X}$ and ${\boldsymbol Y}$ given another random vector $\boldsymbol Z$ using the ball divergence. Our measure characterizes…

Statistics Theory · Mathematics 2024-08-01 Bilol Banerjee , Bhaswar B. Bhattacharya , Anil K. Ghosh

We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…

Methodology · Statistics 2026-01-28 Jinyuan Chang , Yue Du , Jing He , Qiwei Yao

We propose a sequential, anytime-valid method to test the conditional independence of a response $Y$ and a predictor $X$ given a random vector $Z$. The proposed test is based on e-statistics and test martingales, which generalize likelihood…

Methodology · Statistics 2023-02-22 Peter Grünwald , Alexander Henzi , Tyron Lardy

We study the problem of testing the null hypothesis that X and Y are conditionally independent given Z, where each of X, Y and Z may be functional random variables. This generalises testing the significance of X in a regression model of…

Statistics Theory · Mathematics 2023-09-27 Anton Rask Lundborg , Rajen D. Shah , Jonas Peters

Tests of conditional independence (CI) underpin a number of important problems in machine learning and statistics, from causal discovery to evaluation of predictor fairness and out-of-distribution robustness. Shah and Peters (2020) showed…

Machine Learning · Statistics 2025-12-17 Zheng He , Roman Pogodin , Yazhe Li , Namrata Deka , Arthur Gretton , Danica J. Sutherland

The standard method to check for the independence of two real-valued random variables -- demonstrating that the bivariate joint distribution factors into the product of its marginals -- is both necessary and sufficient. Here we present a…

Probability · Mathematics 2021-11-30 David Draper , Erdong Guo , Robert Lund , Jon Woody

An important aspect of multiple hypothesis testing is controlling the significance level, or the level of Type I error. When the test statistics are not independent it can be particularly challenging to deal with this problem, without…

Statistics Theory · Mathematics 2009-03-04 Sandy Clarke , Peter Hall

We propose a new nonparametric test for the supposition of independence between two continuous random variables. The test is based on the size of the longest increasing subsequence of a random permutation. We identified the independence…

Methodology · Statistics 2015-03-13 Jesus E. Garcia , Veronica A. Gonzalez-Lopez

We propose a new conditional dependence measure and a statistical test for conditional independence. The measure is based on the difference between analytic kernel embeddings of two well-suited distributions evaluated at a finite set of…

Machine Learning · Statistics 2022-06-17 Meyer Scetbon , Laurent Meunier , Yaniv Romano

This paper is concerned with the problem of conditional independence testing for discrete data. In recent years, researchers have shed new light on this fundamental problem, emphasizing finite-sample optimality. The non-asymptotic viewpoint…

Statistics Theory · Mathematics 2023-10-31 Ilmun Kim , Matey Neykov , Sivaraman Balakrishnan , Larry Wasserman

This paper introduces the \textit{weighted partial copula} function for testing conditional independence. The proposed test procedure results from these two ingredients: (i) the test statistic is an explicit Cramer-von Mises transformation…

Methodology · Statistics 2021-02-15 Pascal Bianchi , Kevin Elgui , François Portier

Testing conditional independence between two random vectors given a third is a fundamental and challenging problem in statistics, particularly in multivariate nonparametric settings due to the complexity of conditional structures. We…

Machine Learning · Statistics 2025-07-28 Chenxuan He , Yuan Gao , Liping Zhu , Jian Huang

We consider testing marginal independence versus conditional independence in a trivariate Gaussian setting. The two models are non-nested and their intersection is a union of two marginal independences. We consider two sequences of such…

Statistics Theory · Mathematics 2020-10-23 F. Richard Guo , Thomas S. Richardson

We study the problem of conditional two-sample testing, which aims to determine whether two populations have the same distribution after accounting for confounding factors. This problem commonly arises in various applications, such as…

Machine Learning · Statistics 2026-05-05 Seongchan Lee , Suman Cha , Ilmun Kim