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Despite the popularity of feature importance (FI) measures in interpretable machine learning, the statistical adequacy of these methods is rarely discussed. From a statistical perspective, a major distinction is between analyzing a…

Machine Learning · Statistics 2023-05-03 Kristin Blesch , David S. Watson , Marvin N. Wright

Conditional Feature Importance (CFI) is a classical variable importance measure that accounts for the relationship between the studied feature and the others. However, CFI has not yet been studied from a theoretical perspective because the…

Statistics Theory · Mathematics 2026-02-03 Angel Reyero-Lobo , Pierre Neuvial , Bertrand Thirion

Conditional independence (CI) testing is a fundamental and challenging task in modern statistics and machine learning. Many modern methods for CI testing rely on powerful supervised learning methods to learn regression functions or Bayes…

Machine Learning · Statistics 2023-10-31 Felipe Maia Polo , Yuekai Sun , Moulinath Banerjee

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

Variable importance assessment has become a crucial step in machine-learning applications when using complex learners, such as deep neural networks, on large-scale data. Removal-based importance assessment is currently the reference…

Machine Learning · Computer Science 2023-10-27 Ahmad Chamma , Denis A. Engemann , Bertrand Thirion

Conformal prediction provides rigorous distribution-free finite-sample guarantees for marginal coverage under the assumption of exchangeability, but may exhibit systematic undercoverage or overcoverage for specific subpopulations. Assessing…

Methodology · Statistics 2026-04-24 Zheng Zhou , Xiangfei Zhang , Chongguang Tao , Yuhong Yang

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 Mutual Information (CMI) is a measure of conditional dependence between random variables X and Y, given another random variable Z. It can be used to quantify conditional dependence among variables in many data-driven inference…

Machine Learning · Computer Science 2019-06-10 Sudipto Mukherjee , Himanshu Asnani , Sreeram Kannan

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

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

Variable importance plays a pivotal role in interpretable machine learning as it helps measure the impact of factors on the output of the prediction model. Model agnostic methods based on the generation of "null" features via permutation…

Accurate conditional prediction in the regression setting plays an important role in many real-world problems. Typically, a point prediction often falls short since no attempt is made to quantify the prediction accuracy. Classically, under…

Methodology · Statistics 2025-09-04 Kejin Wu , Dimitris N. Politis

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

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

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

Motivation: Machine learning based prediction of compound-protein interactions (CPIs) is important for drug design, screening and repurposing studies and can improve the efficiency and cost-effectiveness of wet lab assays. Despite the…

Quantitative Methods · Quantitative Biology 2022-02-02 Adiba Yaseen , Imran Amin , Naeem Akhter , Asa Ben-Hur , Fayyaz Minhas

Structure learning of Conditional Random Fields (CRFs) can be cast into an L1-regularized optimization problem. To avoid optimizing over a fully linked model, gain-based or gradient-based feature selection methods start from an empty model…

Machine Learning · Computer Science 2014-07-01 Ni Lao , Jun Zhu

Testing (conditional) independence of multivariate random variables is a task central to statistical inference and modelling in general - though unfortunately one for which to date there does not exist a practicable workflow. State-of-art…

Machine Learning · Statistics 2018-05-01 Samuel Burkart , Franz J Király

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

Notions of counterfactual invariance (CI) have proven essential for predictors that are fair, robust, and generalizable in the real world. We propose graphical criteria that yield a sufficient condition for a predictor to be…

Machine Learning · Computer Science 2024-08-12 Francesco Quinzan , Cecilia Casolo , Krikamol Muandet , Yucen Luo , Niki Kilbertus
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