Learning AMP Chain Graphs and some Marginal Models Thereof under Faithfulness: Extended Version

TL;DR

This paper introduces algorithms for learning AMP chain graphs and a new family of graphical models called MCCGs, explores their properties, and discusses limitations of extending Meek's conjecture to AMP CGs.

Contribution

It presents a constraint-based algorithm for learning AMP chain graphs and MCCGs, introduces MCCGs as a new graphical model family, and analyzes their properties and equivalence classes.

Findings

A constraint-based algorithm for AMP CGs under faithfulness.

Introduction of MCCGs combining undirected and bidirected edges.

A graphical criterion for reading dependencies from MCCGs.

Abstract

This paper deals with chain graphs under the Andersson-Madigan-Perlman (AMP) interpretation. In particular, we present a constraint based algorithm for learning an AMP chain graph a given probability distribution is faithful to. Moreover, we show that the extension of Meek's conjecture to AMP chain graphs does not hold, which compromises the development of efficient and correct score+search learning algorithms under assumptions weaker than faithfulness. We also introduce a new family of graphical models that consists of undirected and bidirected edges. We name this new family maximal covariance-concentration graphs (MCCGs) because it includes both covariance and concentration graphs as subfamilies. However, every MCCG can be seen as the result of marginalizing out some nodes in an AMP CG. We describe global, local and pairwise Markov properties for MCCGs and prove their equivalence. We characterize when two MCCGs are Markov equivalent, and show that every Markov equivalence class of MCCGs has a distinguished member. We present a constraint based algorithm for learning a MCCG a given probability distribution is faithful to. Finally, we present a graphical criterion for reading dependencies from a MCCG of a probability distribution that satisfies the graphoid properties, weak transitivity and composition. We prove that the criterion is sound and complete in certain sense.