Local-Global LWF Chain Graph Structure Learning Algorithm Based on Constraints

LWF chain graph structure learning aims to find the parents, children, neighbours and spouses of all nodes in the chain graph. Currently, the state-of-the-art LWF chain graph structure learning algorithms obtain the local structure of nodes to learn the global network structure based on Growing-Shrinking (GS) idea. The conditional independence test of these algorithms takes the whole Markov blanket (MB) as the condition set. In order to ensure the reliability of conditional independence test, the number of samples is required to be exponential level of the size of Markov blanket, which makes the data efficiency of the algorithm poor. To alleviate this problem, we propose a Local-Global LWF chain graph structure learning algorithm based on constraints, which reduces the requirement of sample size of data by iterative learning adjacencies and spouses; while learning adjacencies, it further improves the accuracy of the conditional independence test by backward strategy. The basic idea of the algorithm as follows: firstly, the Markov blanket of each node in the network is learned, and the Markov blanket learning of node is divided into learning the adjacencies and the spouses; secondly, we use the Markov blanket information of nodes to recover the network skeleton and take advantage of conditional independent test to discover its complexes, which restores the chain graph structure, according to the characteristics of directed edges of chain graph complexes. Theoretical analysis demonstrates the correctness of the algorithm. Moreover, experiments on the generated datasets and standard datasets show the effectiveness of the algorithm. © 2023 Chinese Institute of Electronics. All rights reserved.