Learning the structure of multivariate regression chain graphs by testing complete separators in prime blocks

This paper introduces an algorithm to construct a bidirectional causal graph using an augmented graph. The algorithm decomposes the augmented graph, significantly reducing the size of the variable set required for conditional independence testing. Simultaneously, it preserves the fundamental structure of the augmented graph after decomposition, saving time and cost in constructing a global skeleton graph. Through experiments on discrete and continuous datasets, the algorithm demonstrates a clear advantage in runtime compared to traditional methods. In large-scale sparse networks, the training time is only about one-tenth of traditional methods. Additionally, the algorithm shows improvement in terms of construction error. Since the input to the algorithm is an augmented graph, this paper also discusses the impact on construction error when using both real and generated augmented graphs as input. Furthermore, the concept of markov blanket is extended to multivariate regression chain graphs, providing a method for rapidly constructing augmented graphs given certain prior knowledge.