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.

一个马尔可夫毯族，如果纯粹作为一组变量子集学习，可能与任何贝叶斯网络不一致。这种不一致可能对基于马尔可夫毯的结构学习产生负面影响。在本文中，我们建议使用图道德检查马尔可夫毯一致性。我们定义了一个道德图的替代概念——弱递归简单性——而不依赖于贝叶斯网络。虽然一般来说决定一个无向图是否道德是 NP 完全的，但我们提出了线性和二次时间算法来分别为最大度 3 和 4 的图确定道德。此外，我们证明了对于最大度数高于 4 的图，该问题仍然是 NP 完全的，因此此类问题没有剩余的未知复杂度。