Learning marginal AMP chain graphs under faithfulness revisited

•We present a constraint based algorithm for learning MAMP chain graphs.•The algorithm assumes faithfulness.•The MAMP chain graph learned is a distinguished member of its equivalence class.•We show that the extension of Meek's conjecture to MAMP chain graphs does not hold.

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 Meek's 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.