σ-Maximal Ancestral Graphs
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Abstract (arXiv)
Maximal Ancestral Graphs (MAGs) provide an abstract representation of Directed Acyclic Graphs (DAGs) with latent (selection) variables. These graphical objects encode information about ancestral relations and d-separations of the DAGs they represent. This abstract representation has been used amongst others to prove the soundness and completeness of the FCI algorithm for causal discovery, and to derive a do-calculus for its output. One significant inherent limitation of MAGs is that they rule out the possibility of cyclic causal relationships. In this work, we address that limitation. We introduce and study a class of graphical objects that we coin ''σ-Maximal Ancestral Graphs'' (''σ-MAGs''). We show how these graphs provide an abstract representation of (possibly cyclic) Directed Graphs (DGs) with latent (selection) variables, analogously to how MAGs represent DAGs. We study the properties of these objects and provide a characterization of their Markov equivalence classes.
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References · 8
- 2013Causal Inference in the Presence of Latent Variables and Selection Biascited by 166
- 2016Foundations of Structural Causal Models with Cycles and Latent Variablescited by 134
- 2017Markov Properties for Graphical Models with Cycles and Latent Variablescited by 32
- 2020Constraint-Based Causal Discovery using Partial Ancestral Graphs in the presence of Cyclescited by 31
- 2013Directed Cyclic Graphical Representations of Feedback Modelscited by 28
- 2018A Constraint-Based Algorithm For Causal Discovery with Cycles, Latent Variables and Selection Biascited by 16
- 2023Establishing Markov Equivalence in Cyclic Directed Graphscited by 6
- 2013A Constraint Propagation Approach to Probabilistic Reasoningcited by 3
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