Chain graphs structure learning given local background knowledge

Abstract

Chain graphs structure learning aims to identify and infer causal relations and symmetric association relations between variables in data. However, existing chain graphs structure learning algorithms cannot uniquely determine the causal relations from data among some variables due to the independence of these variables corresponding to multiple structures, making them only learn Markov equivalence classes of chain graphs. To alleviate this issue, we propose a Chain Graphs structure Learning algorithm Given local background Knowledge (CGLGK). CGLGK initially learns the adjacencies and spouses of variables, constructs the skeleton of chain graphs using the adjacencies, corrects the connections between variables in the skeleton guided by local background knowledge, and orients the edges using the adjacencies and spouses to obtain the Markov equivalence classes of chain graphs. Next, CGLGK fuses local background knowledge with the learned Markov equivalence classes to obtain new knowledge. Finally, it utilizes the local valid orientation rule to orient edges within the Markov equivalence classes based on the updated knowledge, resulting in the final chain graphs structure. Meanwhile, we conducted the theoretical analysis to prove the correctness of CGLGK, and its effectiveness is verified by comparison with the classical and state-of-the-art algorithms on synthetic and real data.