Identifying Independencies in Causal Graphs with Feedback

By Judea Pearl, Rina Dechter. 1996

We show that the d-separation criterion constitutes a valid test for conditional independence relationships that are induced by feedback systems involving discrete variables.

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Citations in the corpus

From Ordinary Differential Equations to Structural Causal Models: the deterministic case (2013, background): “Nevertheless, several algorithms (starting from diﬀerent assumptions) have been proposed for inferring cyclic causal models from observational data (Richardson, 1996; Lacerda et al., 2008; Schmidt and Murphy, 2009; Itani et al., 2010; Mooij et al., 2011).”
Modeling Discrete Interventional Data using Directed Cyclic Graphical Models (2009, background): “Pearl and Dechter (1996) prove an analogous result that d-separation is valid for feedback systems involving discrete variables.”
Comorbidity: A network perspective (2010, background): “The theory of cyclic graphical models is difficult and underdeveloped, and for binary variables no adequate search procedure is available, but the target article does not engage what is known (e.g., Lacerda et al. 2008; Pearl & Dechter 1996; Richardson 1996).”
Structure learning in causal cyclic networks (2008, background): “Key developments (Spirtes, 1995) and (Koster, 1996), endowed DCGs with some of the properties of their DAG counterparts, and it was also shown that some SEMs are amenable to the same analysis (Spirtes, 1995; Pearl and Dechter, 1996).”
A New Inferential Test for Path Models Based on Directed Acyclic Graphs (2000, background): “Pearl and Dechter (1996) have recently shown that d-separation implies statistical independence in cyclic directed graphs involving nonlinear causal relationships if all the random variables are discrete.”
Learning Optimal Causal Graphs with Exact Search (2018, background): “…(i.e. the structural equations for a set of nodes and their ancestors) has a unique solution (Forré and Mooij (2017): Thm 3.8.12 on p. 112, see also Pearl and Dechter (1996), Neal (2000)).1 Under the commonly used faithfulness assumption (Spirtes et al., 2000), statistical dependence becomes…”
A Simple Constraint-Based Algorithm for Efficiently Mining Observational Databases for Causal Relationships (1997, methodology): “Consider extending the graphical representation presented thus far to include directed cycles, as is done by Richardson (1996) and by Pearl and Dechter (1996).”
Foundations of structural causal models with cycles and latent variables (2016, background): “The discrete case fixes the erroneous theorem by Pearl and Dechter [49], for which a counterexample was found by Neal [46], by adding the ancestral unique solvability condition, and extends it to allow for bidirected edges in the graph.”
Joint Causal Inference from Multiple Contexts (2016, background): “The discrete case fixes the erroneous theorem by Pearl and Dechter (1996), for which a counterexample was found by Neal (2000), by adding the unique solvability condition, and extends it to allow for latent common causes.”
Partial correlation for functional brain interactivity investigation in functional MRI (2006, background): “These problems, which are critical for directed acyclic graphs, are even more crucial for cyclic graphs, which are commonly used in effective connectivity modeling, while many theoretical questions remain unsolved (Spirtes, 1995; Pearl and Dechter, 1996; Neal, 2000).”
Discovering Cyclic Causal Models with Latent Variables: A General SAT-Based Procedure (2013, background): “A general characterization of the parameterizations of cyclic models (with latent variables), for which the correspondence between d-separation and probabilistic independence holds, is not known (Pearl and Dechter, 1996; Neal, 2000).”