Causal Inference in the Presence of Latent Variables and Selection Bias

By Peter Spirtes, Christopher Meek, Thomas S. Richardson. 1995

We show that there is a general, informative and reliable procedure for discovering causal relations when, for all the investigator knows, both latent variables and selection bias may be at work. Given information about conditional independence and dependence relations between measured variables, even when latent variables and selection bias may be present, there are sufficient conditions for reliably concluding that there is a causal path from one variable to another, and sufficient conditions for reliably concluding when no such causal path exists.

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Citations in the corpus

Causal Reasoning for Algorithmic Fairness (2018, background): “But selection bias cuts deeper than that, and more recently causal knowledge has been formally brought in to understand the role of such biases [2, 40].”
Counterfactual Normalization: Proactively Addressing Dataset Shift and Improving Reliability Using Causal Mechanisms (2018, background): “For example, Spirtes et al. (1995) learn the structure of the causal DAG from data affected by selection bias.”
Order-independent constraint-based causal structure learning (2012, methodology): “The grey line labelled as RG represents the random guessing. stable plus stability selection (with or without permuted variable orderings) produces the best ﬁt over all results. and RFCI-algorithms remain valid for their modiﬁcations under the same conditions.”
Causal Structure Learning (2017, methodology): “The Fast Causal Inference (FCI) algorithm Spirtes et al. (1999, 2000) is a modiﬁcation of the PC algorithm that drops the assumption of causal suﬃciency by allowing arbitrarily many hidden variables.”
DAG-GNN: DAG Structure Learning with Graph Neural Networks (2019, methodology): “Popular algorithms include SGS (Spirtes et al., 2000b), PC (Spirtes et al., 2000b), IC (Pearl, 2003), and FCI (Spirtes et al., 1995; Zhang, 2008).”
Algorithmic Fairness (2020, background): “Another approach to improve fairness using causal reasoning is to provide an understanding of how to perform imputation of missing values or how to repair a dataset that contains sample or selection bias [10, 127].”
Discovering Cyclic Causal Models with Latent Variables: A General SAT-Based Procedure (2013, methodology): “In recent years, many approaches to this causal discovery problem have been suggested (Spirtes et al., 1999; Richardson and Spirtes, 1999; Schmidt and Murphy, 2009; Claassen and Heskes, 2010; Peters et al., 2010; Triantaﬁllou et al., 2010), building on the framework of causal Bayes networks…”
A Simple Constraint-Based Algorithm for Efficiently Mining Observational Databases for Causal Relationships (1997, methodology): “In theory, however, the PC and FCI methods can detect such induced selection bias (Spirtes et al., 1995), and thus, avoid reporting incorrect causal constraints.”
Learning Sparse Causal Models is not NP-hard (2013, methodology): “To tackle this problem, Spirtes et al. (1999) developed the so-called Fast Causal Inference (FCI) algorithm that introduces an additional stage to the adjacency search.”
A Characterization of Markov Equivalence Classes for Directed Acyclic Graphs with Latent Variables (2007, methodology): “4We call it PFCI because R0 − R4 are essentially the rules used in the FCI algorithm given in Spirtes et al. (1999). yet the PAG of [G].”
A Review on Fairness in Machine Learning (2022, background): “Another approach to improve fairness using causal reasoning is to provide an understanding of how to perform imputation of missing values or how to repair a dataset that contains sample or selection bias [13, 191].”
Comparison of Strategies for Scalable Causal Discovery of Latent Variable Models from Mixed Data (2018, methodology): “We originally developed FCI, which learns a causal PAG from data that may include latent variables [27].”
A Survey of Learning Causality with Data: Problems and Methods (2018, methodology): “To take unobserved confounders into consideration, algorithms are introduced to search through an extended space of causal graphs such as FCI and its extensions [30, 130].”
Foundations of structural causal models with cycles and latent variables (2016, methodology): “Recently it has been shown that even the well-known Fast Causal Inference (FCI) algorithm [69, 75] is directly applicable to simple SCMs [41] and provides a consistent estimate of the Markov equivalence class (under the faithfulness assumption).”