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Inducing Sets: A New Perspective for Ancestral Graph Markov Models

Andrews, Bryan James (2022) Inducing Sets: A New Perspective for Ancestral Graph Markov Models. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Directed acyclic graphs (DAGs) and their corresponding Markov models have become widely studied and applied in the fields of statistics and causality. The simple directed structure of these models facilitates systematic learning procedures and provides an interpretable representation for causal relationships. However, DAGs are ill-equipped to handle latent variables without explicitly invoking them. This manifests as a lack of stability under marginalization and conditioning and a disparity between statistically and causally valid models. Meanwhile, latent confounding and selection effects occur with some regularity in many domains. The family of maximal ancestral graphs (MAGs) extends the family of DAGs by implicitly taking latent variables into account. In fact, the family of MAGs constitutes the smallest superset of the family of DAGs that is stable under marginalization and conditioning. Accordingly, MAGs and their corresponding Markov models---ancestral graph Markov models---provide a natural choice for statistical and causal modeling in systems with latent confounding and selection effects.

In this work we introduce inducing sets as a new perspective for reasoning about ancestral graph Markov models. In particular, we derive and study m-connecting sets which are a special case of inducing sets and provide an alternative representation for MAGs. We show that m-connecting sets admit a characterization of Markov equivalence for MAGs and a factorization criterion equivalent to the global Markov property for directed MAGs. Using the factorization criterion, we formulate a consistent probabilistic score with a closed-form for the Markov models of directed MAGs. Ultimately, we design a local causal discovery algorithm called the ancestral probability (AP) procedure which estimates the posterior probabilities of ancestral relationships. We evaluate the AP procedure on synthetically generated data and a real data set measuring airborne pollutants, cardiovascular health, and respiratory health.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Andrews, Bryan Jamesbja43@pitt.edubja43
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairCooper,
Committee MemberTriantafillou,
Committee MemberPanagiotis,
Committee MemberSpirtes,
Committee MemberRichardson,
Date: 24 February 2022
Date Type: Publication
Defense Date: 30 August 2021
Approval Date: 24 February 2022
Submission Date: 13 October 2021
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 300
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Intelligent Systems
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: Ancestral Graph Markov Models, Factorization of Probability Densities, Causal Discovery
Date Deposited: 24 Feb 2022 15:31
Last Modified: 24 Feb 2022 15:31

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