# Identifiability and Consistent Estimation for Gaussian Chain Graph Models

arXiv: https://arxiv.org/abs/2303.01031 · HTML: https://mlsanity.com/paper/2303.01031/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Mar 2023.

## Built on by (most cited first, 1 of 1)

- [Time Series Gaussian Chain Graph Models](https://mlsanity.com/paper/2604.07018/) (2026)

## Abstract (arXiv)

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 literature, possibly due to the lack of identifiability conditions between undirected and directed edges. In this paper, 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.