Generating Markov Equivalent Maximal Ancestral Graphs by Single Edge Replacement
This work addresses a theoretical problem in causal inference for researchers dealing with hidden variables, but it appears incremental as it builds on existing equivalence concepts without broad practical application.
The paper tackles the problem of generating Markov equivalent maximal ancestral graphs (MAGs) by identifying conditions under which edge types (arrows or bi-directed edges) can be modified through reversal or interchange while preserving Markov equivalence, focusing on MAGs without undirected edges.
Maximal ancestral graphs (MAGs) are used to encode conditional independence relations in DAG models with hidden variables. Different MAGs may represent the same set of conditional independences and are called Markov equivalent. This paper considers MAGs without undirected edges and shows conditions under which an arrow in a MAG can be reversed or interchanged with a bi-directed edge so as to yield a Markov equivalent MAG.