Primary Submission Category: Causal Discovery
Causal discovery with expert knowledge
Authors: Aparajithan Venkateswaran, Emilija Perkovic,
Presenting Author: Aparajithan Venkateswaran*
We consider Markov equivalence classes of maximal ancestral graphs (MAGs) and their restrictions. MAGs are directed mixed graphs used to model conditional independence constraints between a set of observed variables which correspond to nodes in the graph. All MAGs that imply the same set of conditional independence relationships form a Markov equivalence class, which can be uniquely represented by a partially oriented graph (essential graph). Past work has seen the development of algorithms for learning an essential graph from observational data. Recently, there has been interest in learning restrictions of the Markov equivalence class under specific kinds of causal background knowledge. In this work, we focus on restrictions of the Markov equivalence class formed by fixing certain edgemarks.
First, we generalize a property previously formalized by Zhao et al. [2005] and prove a conjecture by Ali et al. [2009] for MAGs in a Markov equivalence class. Second, we incorporate edgemark background knowledge into an essential graph analogous to Meek [1995]. We prove soundness for two new orientation rules in addition to the previously established rules of Spirtes et al. [1999] and Zhang [2008]. We further refine some of the orientation rules of Zhang [2008] in our setting. Finally, we provide a sound algorithm to restrict the equivalence class of MAGs using background knowledge. We show that our algorithm is complete for a special case and conjecture that it is true for all graphs.