The Complexity of Morality: Checking Markov Blanket Consistency with DAGs via Morality
This work addresses theoretical graph and Bayesian network problems, with incremental contributions to computational complexity analysis.
The paper establishes a bijection between consistent Markov blanket families and moral graphs, introducing new graph properties and proving polynomial-time decidability for graphs with maximum degree less than 5, while showing NP-completeness for higher degrees.
A family of Markov blankets in a faithful Bayesian network satisfies the symmetry and consistency properties. In this paper, we draw a bijection between families of consistent Markov blankets and moral graphs. We define the new concepts of weak recursive simpliciality and perfect elimination kits. We prove that they are equivalent to graph morality. In addition, we prove that morality can be decided in polynomial time for graphs with maximum degree less than $5$, but the problem is NP-complete for graphs with higher maximum degrees.