Identifiability and Consistent Estimation for Gaussian Chain Graph Models

Ruixuan,Zhao1; Haoran,Zhang2; Junhui,Wang3

2024-02-14

10.1080/01621459.2024.2304692

Journal of the American Statistical Association   影响因子和分区

0162-1459

1537-274X

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.

Causal inference Directed acyclic graph Gaussian graphical model Low-rank plus sparse decomposition Tangent space

SCI

英语

通讯

Mathematics

Statistics & Probability

WOS:001162620100001

Taylor & Francis

MATHEMATICS

人工提交

1.香港城市大学
2.南方科技大学
3.香港中文大学

Ruixuan,Zhao,Haoran,Zhang,Junhui,Wang. Identifiability and Consistent Estimation for Gaussian Chain Graph Models[J]. Journal of the American Statistical Association,2024:1-12.

Ruixuan,Zhao,Haoran,Zhang,&Junhui,Wang.(2024).Identifiability and Consistent Estimation for Gaussian Chain Graph Models.Journal of the American Statistical Association,1-12.

Ruixuan,Zhao,et al."Identifiability and Consistent Estimation for Gaussian Chain Graph Models".Journal of the American Statistical Association (2024):1-12.