报告题目：Chain graph models: identifiability, estimation and asymptotics

报告时间：2024.06.27   15:00-16:00

报  告 人 ：王军辉 教授 香港中文大学

报告地点：理学院东北楼二楼报告厅（209）

Abstract：In this talk, we consider a flexible chain graph (CG) model, which admits both undirected and directed edges in one graph and thus can encode much more diverse relations among objects. We first establish the identifiability conditions for the CG model through a low rank plus sparse matrix decomposition, where the sparse matrix implies the sparse undirected edges within each chain component and the low rank matrix implies the presence of hub nodes with multiple children or parents. On this ground, we develop an efficient estimation method for reconstructing the CG structure, which first identifies the chain components via estimated undirected edges, determines the causal ordering of the chain components, and eventually estimates the directed edges among the chain components. Its theoretical properties will be discussed in terms of both asymptotic and finite-sample probability bounds on model estimation and graph reconstruction. The advantage of the proposed method is also demonstrated through extensive numerical experiments on both synthetic data and the Standard & Poor's 500 index data.