Learning marginal AMP chain graphs under faithfulness revisited

Marginal AMP chain graphs are a recently introduced family of models that is based on graphs that may have undirected, directed and bidirected edges. They unify and generalize the AMP and the multivariate regression interpretations of chain graphs. In this paper, we present a constraint based algorithm for learning a marginal AMP chain graph from a probability distribution which is faithful to it. We show that the marginal AMP chain graph returned by our algorithm is a distinguished member of its Markov equivalence class. We also show that our algorithm performs well in practice. Finally, we show that the extension of Meeks conjecture to marginal AMP chain graphs does not hold, which compromises the development of efficient and correct score+search learning algorithms under assumptions weaker than faithfulness. (C) 2015 Elsevier Inc. All rights reserved.Funding Agencies|Center for Industrial Information Technology [09.01]; Swedish Research Council [2010-4808]; Spanish Ministry of Economy and Competitiveness [TIN2013-46638-C3-2-P]; European Regional Development Fund (FEDER)