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Testing for the conditional independence structure in data is a fundamental and critical task in statistics and machine learning, which finds natural applications in causal discovery - a highly relevant problem to many scientific…

Machine Learning · Statistics 2025-03-03 Bao Duong , Nu Hoang , Thin Nguyen

Conventional causal discovery methods rely on centralized data, which is inconsistent with the decentralized nature of data in many real-world situations. This discrepancy has motivated the development of federated causal discovery (FCD)…

Machine Learning · Computer Science 2024-02-28 Loka Li , Ignavier Ng , Gongxu Luo , Biwei Huang , Guangyi Chen , Tongliang Liu , Bin Gu , Kun Zhang

Conditional independence testing (CIT) is essential for reliable scientific discovery. It prevents spurious findings and enables controlled feature selection. Recent CIT methods have used machine learning (ML) models as surrogates of the…

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

This paper is concerned with test of the conditional independence. We first establish an equivalence between the conditional independence and the mutual independence. Based on the equivalence, we propose an index to measure the conditional…

Methodology · Statistics 2021-05-18 Zhanrui Cai , Runze Li , Yaowu Zhang

Learning causal structure from observational data is especially challenging when latent variables or selection bias are present. The Fast Causal Inference (FCI) algorithm addresses this setting but performs exhaustive conditional…

Machine Learning · Computer Science 2025-11-06 Joseph Ramsey , Bryan Andrews , Peter Spirtes

Scientific practice typically involves repeatedly studying a system, each time trying to unravel a different perspective. In each study, the scientist may take measurements under different experimental conditions (interventions,…

Machine Learning · Statistics 2014-03-11 Sofia Triantafillou , Ioannis Tsamardinos

Causal discovery methods seek to identify causal relations between random variables from purely observational data, as opposed to actively collected experimental data where an experimenter intervenes on a subset of correlates. One of the…

Machine Learning · Computer Science 2021-02-08 Samir Wadhwa , Roy Dong

Causal discovery from observational data is a fundamental task in artificial intelligence, with far-reaching implications for decision-making, predictions, and interventions. Despite significant advances, existing methods can be broadly…

Machine Learning · Computer Science 2026-02-06 Jincheng Zhou , Mengbo Wang , Anqi He , Yumeng Zhou , Hessam Olya , Murat Kocaoglu , Bruno Ribeiro

Inferring causal structure from data is a challenging task of fundamental importance in science. Observational data are often insufficient to identify a system's causal structure uniquely. While conducting interventions (i.e., experiments)…

Combinatorial interaction testing (CIT) is a well-known technique, but the industrial experience is needed to determine its effectiveness in different application domains. We present a case study introducing a unified framework for…

Software Engineering · Computer Science 2019-03-14 Bestoun S. Ahmed , Amador Pahim , Cleber R. Rosa Junior , D. Richard Kuhn , Miroslav Bures

Deep ensembles (DE) have emerged as a powerful approach for quantifying predictive uncertainty and distinguishing its aleatoric and epistemic components, thereby enhancing model robustness and reliability. However, their high computational…

Machine Learning · Computer Science 2025-11-19 Kaizheng Wang , Fabio Cuzzolin , David Moens , Hans Hallez

Constraint-based causal discovery from limited data is a notoriously difficult challenge due to the many borderline independence test decisions. Several approaches to improve the reliability of the predictions by exploiting redundancy in…

Machine Learning · Computer Science 2017-01-27 Sara Magliacane , Tom Claassen , Joris M. Mooij

Causality is essential for understanding complex systems, such as the economy, the brain, and the climate. Constructing causal graphs often relies on either data-driven or expert-driven approaches, both fraught with challenges. The former…

Artificial Intelligence · Computer Science 2024-06-12 Kai-Hendrik Cohrs , Gherardo Varando , Emiliano Diaz , Vasileios Sitokonstantinou , Gustau Camps-Valls

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

Learning causal relations from observational data is a fundamental problem with wide-ranging applications across many fields. Constraint-based methods infer the underlying causal structure by performing conditional independence tests.…

Machine Learning · Computer Science 2026-03-24 Marc Franquesa Monés , Jiaqi Zhang , Caroline Uhler

Learning graphical conditional independence structures from nonlinear, continuous or mixed data is a central challenge in machine learning and the sciences, and many existing methods struggle to scale to thousands of samples or hundreds of…

Machine Learning · Statistics 2025-11-05 Joseph Ramsey , Bryan Andrews , Peter Spirtes

Learning causal structure is useful in many areas of artificial intelligence, including planning, robotics, and explanation. Constraint-based structure learning algorithms such as PC use conditional independence (CI) tests to infer causal…

Machine Learning · Computer Science 2022-11-15 Erica Cai , Andrew McGregor , David Jensen

The growing complexity of safety-relevant systems causes an increasing effort for safety assurance. The reduction of development costs and time-to-market, while guaranteeing safe operation, is therefore a major challenge. In order to enable…

Software Engineering · Computer Science 2021-06-08 Sebastian Reiter , Marc Zeller , Kai Hoefig , Alexander Viehl , Oliver Bringmann , Wolfgang Rosenstiel

Conditional randomization tests (CRTs) assess whether a variable $x$ is predictive of another variable $y$, having observed covariates $z$. CRTs require fitting a large number of predictive models, which is often computationally…

Methodology · Statistics 2023-04-12 Mukund Sudarshan , Aahlad Manas Puli , Wesley Tansey , Rajesh Ranganath

Causal inference is a fundamental research topic for discovering the cause-effect relationships in many disciplines. However, not all algorithms are equally well-suited for a given dataset. For instance, some approaches may only be able to…

Machine Learning · Computer Science 2024-03-11 Zhipeng Ma , Marco Kemmerling , Daniel Buschmann , Chrismarie Enslin , Daniel Lütticke , Robert H. Schmitt