The difficulty of being moral

A family of Markov blankets, if learned purely as a set of subsets of variables, may not be consistent with any Bayesian network. This inconsistency may have a negative impact on Markov blanket-based structure learning. In this paper, we propose checking Markov blanket consistency using graph morality. We define an alternative concept of moral graph - weak recursive simpliciality - without relying on Bayesian networks. Although it is NP-complete to decide if an undirected graph in general is moral, we propose linear and quadratic time algorithms for deciding morality for maximum degree 3 and 4 graphs respectively. In addition, we prove that the problem remains NP-complete for graphs with maximum degree higher than 4, hence there are no remaining unknown complexities for this kind of problem. (C) 2021 Elsevier B.V. All rights reserved.