高斯链图模型的可识别性与一致估计
Identifiability and Consistent Estimation for Gaussian Chain Graph Models
AI总结：
针对高斯链图模型边的可识别性不足的问题，本文基于精度矩阵的低秩加稀疏分解建立新可识别性条件，提出高效结构恢复算法，证明其渐近一致性并通过模拟及真实数据实验验证优势。
摘要：
链图模型可在同一个图中同时包含无向边和有向边，其中对称条件依赖关系通过无向边编码，非对称因果关系通过有向边编码。尽管该模型在实际应用中十分常见，但现有文献对其研究仍十分不足，这可能是由于无向边与有向边之间缺乏可识别性条件。本文首先利用精度矩阵的低秩加稀疏分解，为高斯链图模型建立了一组全新的可识别性条件。此外，本文基于上述可识别性条件构建了一种高效的学习算法，可完全恢复链图结构。我们对所提方法开展了理论分析，证明其在精确恢复链图结构方面具有渐近一致性。模拟示例以及标普500指数数据真实应用的数值实验结果，也验证了所提方法的优势。
英文摘要：
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 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
