On Deducing Conditional Independence from d-Separation in Causal Graphs with Feedback (Research Note)

Abstract

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.

References in corpus (2)

• Directed Cyclic Graphical Representations of Feedback Models
• Identifying Independencies in Causal Graphs with Feedback

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• From Ordinary Differential Equations to Structural Causal Models: the deterministic case
• Markov Properties for Graphical Models with Cycles and Latent Variables
• A general framework for cyclic and fine-tuned causal models and their compatibility with space-time
• Impossibility of superluminal signalling in Minkowski space-time does not rule out causal loops
• Dynamic Causal Bayesian Optimization
• On the Foundations of Cycles in Bayesian Networks