Learning AMP Chain Graphs and some Marginal Models Thereof under Faithfulness: Extended Version
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.
Keywords
Cite
@article{arxiv.1303.0691,
title = {Learning AMP Chain Graphs and some Marginal Models Thereof under Faithfulness: Extended Version},
author = {Jose M. Peña},
journal= {arXiv preprint arXiv:1303.0691},
year = {2014}
}
Comments
Changes from v1 to v2: The interpretation of the antecedent of the rule R3 changed, which in turn implied modifying Lemma 6 and Theorem 1. Changes from v2 to v3: Minor improvements in the first 12 pages. A shorter version is to appear in International Journal of Approximate Reasoning, 2014