On deducing conditional independence from d-separation in causal graphs with feedback

By Radford M. Neal. 2000

54 citations recorded by the source corpus.

Pearl and Dechter (1996) claimed that the d-separation criterion for conditional independence in acyclic causal networks also applies to networks of discrete variables that have feedback cycles, provided that the variables of the system are uniquely determined by the random disturbances. I show by example that this is not true in general. Some condition stronger than uniqueness is needed, such as the existence of a causal dynamics guaranteed to lead to the unique solution.

Subfields: Artificial Intelligence, Molecular Biology

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Citations in the corpus

From Ordinary Differential Equations to Structural Causal Models: the deterministic case (2013, background): “Over the years, several attempts have been made to extend the theory to the cyclic case, thereby enabling causal modeling of systems that involve feedback (Spirtes, 1995; Koster, 1996; Pearl and Dechter, 1996; Neal, 2000; Hyttinen et al., 2012).”
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.”
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).”
Learning Optimal Causal Graphs with Exact Search (2018, background): “…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 equivalent to (a type of)…”
Discovering Cyclic Causal Models with Latent Variables: A General SAT-Based Procedure (2013, methodology): “ation 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). Following the standard approach of non-parametric causal discovery algorithms, we use d”
Joint Causal Inference from Multiple Contexts (2016, background): “The possible interventions are not limited to the perfect interventions modeled by the dooperator of Pearl (2009), but can also be more general types of interventions that appear in practice, like mechanism changes (Tian and Pearl, 2001), soft interventions (Markowetz et al.”