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We propose the conditional predictive impact (CPI), a consistent and unbiased estimator of the association between one or several features and a given outcome, conditional on a reduced feature set. Building on the knockoff framework of…

Methodology · Statistics 2021-05-14 David S. Watson , Marvin N. Wright

Conditional independence testing is a key problem required by many machine learning and statistics tools. In particular, it is one way of evaluating the usefulness of some features on a supervised prediction problem. We propose a novel…

Machine Learning · Statistics 2019-08-02 Marco Henrique de Almeida Inácio , Rafael Izbicki , Rafael Bassi Stern

Conditional independence (CI) is central to causal inference, feature selection, and graphical modeling, yet it is untestable in many settings without additional assumptions. Existing CI tests often rely on restrictive structural…

Machine Learning · Computer Science 2025-12-23 Alek Frohlich , Vladimir Kostic , Karim Lounici , Daniel Perazzo , Massimiliano Pontil

Determining conditional independence (CI) relationships between random variables is a fundamental yet challenging task in machine learning and statistics, especially in high-dimensional settings. Existing generative model-based CI testing…

Machine Learning · Computer Science 2025-05-30 Yixin Ren , Chenghou Jin , Yewei Xia , Li Ke , Longtao Huang , Hui Xue , Hao Zhang , Jihong Guan , Shuigeng Zhou

We consider the problem of non-parametric Conditional Independence testing (CI testing) for continuous random variables. Given i.i.d samples from the joint distribution $f(x,y,z)$ of continuous random vectors $X,Y$ and $Z,$ we determine…

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

Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality, testing for conditional independence of continuous variables is particularly…

Machine Learning · Computer Science 2012-02-20 Kun Zhang , Jonas Peters , Dominik Janzing , Bernhard Schoelkopf

For testing conditional independence (CI) of a response Y and a predictor X given covariates Z, the recently introduced model-X (MX) framework has been the subject of active methodological research, especially in the context of MX knockoffs…

Statistics Theory · Mathematics 2022-11-01 Eugene Katsevich , Aaditya Ramdas

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

Detecting conditional independencies plays a key role in several statistical and machine learning tasks, especially in causal discovery algorithms. In this study, we introduce LCIT (Latent representation based Conditional Independence…

Machine Learning · Computer Science 2022-09-07 Bao Duong , Thin Nguyen

In many real-world scenarios, interested variables are often represented as discretized values due to measurement limitations. Applying Conditional Independence (CI) tests directly to such discretized data, however, can lead to incorrect…

Artificial Intelligence · Computer Science 2025-06-11 Boyang Sun , Yu Yao , Xinshuai Dong , Zongfang Liu , Tongliang Liu , Yumou Qiu , Kun Zhang

Conditional independence tests (CI tests) have received special attention lately in Machine Learning and Computational Intelligence related literature as an important indicator of the relationship among the variables used by their models.…

Conditional independence testing (CIT) is a common task in machine learning, e.g., for variable selection, and a main component of constraint-based causal discovery. While most current CIT approaches assume that all variables are numerical…

Machine Learning · Computer Science 2023-11-07 Oana-Iuliana Popescu , Andreas Gerhardus , Jakob Runge

Conditional independence (CI) testing is frequently used in data analysis and machine learning for various scientific fields and it forms the basis of constraint-based causal discovery. Oftentimes, CI testing relies on strong, rather…

Methodology · Statistics 2023-06-21 Wiebke Günther , Urmi Ninad , jonas Wahl , Jakob Runge

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

Independence screening is a powerful method for variable selection for `Big Data' when the number of variables is massive. Commonly used independence screening methods are based on marginal correlations or variations of it. In many…

Statistics Theory · Mathematics 2012-11-02 Emre Barut , Jianqing Fan , Anneleen Verhasselt

We describe a data-efficient, kernel-based approach to statistical testing of conditional independence. A major challenge of conditional independence testing is to obtain the correct test level (the specified upper bound on the rate of…

Machine Learning · Computer Science 2025-09-23 Roman Pogodin , Antonin Schrab , Yazhe Li , Danica J. Sutherland , Arthur Gretton

Conditional-independence-based discovery uses statistical tests to identify a graphical model that represents the independence structure of variables in a dataset. These tests, however, can be unreliable, and algorithms are sensitive to…

Machine Learning · Computer Science 2026-04-21 Philipp M. Faller , Dominik Janzing

This paper develops a model-free sequential test for conditional independence. The proposed test allows researchers to analyze an incoming i.i.d. data stream with any arbitrary dependency structure, and safely conclude whether a feature is…

Methodology · Statistics 2023-02-21 Shalev Shaer , Gal Maman , Yaniv Romano

Testing for conditional independence is a core aspect of constraint-based causal discovery. Although commonly used tests are perfect in theory, they often fail to reject independence in practice, especially when conditioning on multiple…

Machine Learning · Statistics 2019-03-13 Alexander Marx , Jilles Vreeken
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