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This paper proposes a new algorithm for recovery of belief network structure from data handling hidden variables. It consists essentially in an extension of the CI algorithm of Spirtes et al. by restricting the number of conditional…

Artificial Intelligence · Computer Science 2017-07-03 Mieczysław A. Kłopotek

Causally insufficient structures (models with latent or hidden variables, or with confounding etc.) of joint probability distributions have been subject of intense study not only in statistics, but also in various AI systems. In AI, belief…

Artificial Intelligence · Computer Science 2018-06-04 Mieczysław A. Kłopotek

We consider the problem of learning causal information between random variables in directed acyclic graphs (DAGs) when allowing arbitrarily many latent and selection variables. The FCI (Fast Causal Inference) algorithm has been explicitly…

Methodology · Statistics 2012-05-30 Diego Colombo , Marloes H. Maathuis , Markus Kalisch , Thomas S. Richardson

Causal processes in nature may contain cycles, and real datasets may violate causal sufficiency as well as contain selection bias. No constraint-based causal discovery algorithm can currently handle cycles, latent variables and selection…

Machine Learning · Statistics 2018-05-08 Eric V. Strobl

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

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

While feedback loops are known to play important roles in many complex systems, their existence is ignored in a large part of the causal discovery literature, as systems are typically assumed to be acyclic from the outset. When applying…

Statistics Theory · Mathematics 2023-09-18 Joris M. Mooij , Tom Claassen

Confidence intervals (CIs) are instrumental in statistical analysis, providing a range estimate of the parameters. In modern statistics, selective inference is common, where only certain parameters are highlighted. However, this selective…

Methodology · Statistics 2025-09-17 Tzviel Frostig , Yoav Benjamini , Ruth Heller

Causality lays the foundation for the trajectory of our world. Causal inference (CI), which aims to infer intrinsic causal relations among variables of interest, has emerged as a crucial research topic. Nevertheless, the lack of observation…

Machine Learning · Computer Science 2024-06-21 Yaochen Zhu , Yinhan He , Jing Ma , Mengxuan Hu , Sheng Li , Jundong Li

We consider the problem of discovering causal relations from independence constraints selection bias in addition to confounding is present. While the seminal FCI algorithm is sound and complete in this setup, no criterion for the causal…

Machine Learning · Computer Science 2022-03-04 Philip Versteeg , Cheng Zhang , Joris M. Mooij

Causal structure discovery from observational data is fundamental to the causal understanding of autonomous systems such as medical decision support systems, advertising campaigns and self-driving cars. This is essential to solve well-known…

Constraint-based causal discovery methods require a large number of conditional independence (CI) tests, which severely limits their practical applicability due to high computational complexity. Therefore, it is crucial to design an…

Machine Learning · Computer Science 2026-02-10 Shunyu Zhao , Yanfeng Yang , Shuai Li , Kenji Fukumizu

The PC algorithm is the state-of-the-art algorithm for causal structure discovery on observational data. It can be computationally expensive in the worst case due to the conditional independence tests are performed in an…

Machine Learning · Computer Science 2021-09-13 Kai Zhang , Chao Tian , Kun Zhang , Todd Johnson , Xiaoqian Jiang

This article contains detailed proofs and additional examples related to the UAI-2013 submission `Learning Sparse Causal Models is not NP-hard'. It describes the FCI+ algorithm: a method for sound and complete causal model discovery in the…

Machine Learning · Statistics 2014-11-07 Tom Claassen , Joris M. Mooij , Tom Heskes

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

Constraint-based causal discovery (CCD) algorithms require fast and accurate conditional independence (CI) testing. The Kernel Conditional Independence Test (KCIT) is currently one of the most popular CI tests in the non-parametric setting,…

Methodology · Statistics 2017-04-14 Eric V. Strobl , Kun Zhang , Shyam Visweswaran

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

We consider constraint-based methods for causal structure learning, such as the PC-, FCI-, RFCI- and CCD- algorithms (Spirtes et al. (2000, 1993), Richardson (1996), Colombo et al. (2012), Claassen et al. (2013)). The first step of all…

Machine Learning · Statistics 2013-09-30 Diego Colombo , Marloes H. Maathuis

We consider the problem of learning the causal MAG of a system from observational data in the presence of latent variables and selection bias. Constraint-based methods are one of the main approaches for solving this problem, but the…

Machine Learning · Computer Science 2021-10-26 Sina Akbari , Ehsan Mokhtarian , AmirEmad Ghassami , Negar Kiyavash

The standard constraint-based paradigm for causal discovery with incomplete data -- impute first, test second -- is frequently miscalibrated: any consistent conditional independence (CI) test rejects a true null with probability approaching…

Methodology · Statistics 2026-05-07 Thomas S. Robinson , Ranjit Lall
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