Decomposition of structural learning about directed acyclic graphs

In this paper, we propose that structural learning of a directed acyclic graph can be decomposed into problems related to its decomposed subgraphs. The decomposition of structural learning requires conditional independencies, but it does not require that separators are complete undirected subgraphs. Domain or prior knowledge of conditional independencies can be utilized to facilitate the decomposition of structural learning. By decomposition, search for d-separators in a large network is localized to small subnetworks. Thus both the efficiency of structural learning and the power of conditional independence tests can be improved.