Identifiability and Consistent Estimation for Gaussian Chain Graph Models

• 成果类型: Article
• 署名作者: Zhao, Ruixuan; Zhang, Haoran; Wang, Junhui
• 署名单位: City University of Hong Kong; Southern University of Science & Technology; Chinese University of Hong Kong
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2024.2304692
• 发表日期: 2024
• 页码: 3101-3112
• 关键词: bayesian network structure; COVARIANCE ESTIMATION

摘要

The chain graph model admits both undirected and directed edges in one graph, where symmetric conditional dependencies are encoded via undirected edges and asymmetric causal relations are encoded via directed edges. Though frequently encountered in practice, the chain graph model has been largely under investigated in the literature, possibly due to the lack of identifiability conditions between undirected and directed edges. In this article, we first establish a set of novel identifiability conditions for the Gaussian chain graph model, exploiting a low rank plus sparse decomposition of the precision matrix. Further, an efficient learning algorithm is built upon the identifiability conditions to fully recover the chain graph structure. Theoretical analysis on the proposed method is conducted, assuring its asymptotic consistency in recovering the exact chain graph structure. The advantage of the proposed method is also supported by numerical experiments on both simulated examples and a real application on the Standard & Poor 500 index data. Supplementary materials for this article are available online.