Structural discovery amongst a set of variables is of interest in both static and dynamic settings. In the presence of lead-lag dependencies in the data, the dynamics of the system can be represented through a structural equation model (SEM) that simultaneously captures the contemporaneous and temporal relationships amongst the variables, with the former encoded through a directed acyclic graph (DAG) for model identification. In many real applications, a partial ordering amongst the nodes of the DAG is available, which makes it either beneficial or imperative to incorporate it as a constraint in the problem formulation. This paper develops an algorithm that can seamlessly incorporate a priori partial ordering information for solving a linear SEM (also known as Structural Vector Autoregression) under a high-dimensional setting. The proposed algorithm is provably convergent to a stationary point, and exhibits competitive performance on both synthetic and real data sets.

翻译：在变量间的结构发现既适用于静态场景也适用于动态场景。当数据中存在超前滞后依赖关系时，系统动态可通过结构方程模型（SEM）表征，该模型同时捕捉变量间的同期关系和时序关系，其中同期关系通过有向无环图（DAG）编码以实现模型识别。在许多实际应用中，DAG节点间可获得部分排序信息，这使得将其作为约束纳入问题公式化具有优势或必要性。本文开发了一种算法，可在高维场景下无缝融合先验部分排序信息以求解线性SEM（亦称结构向量自回归）。理论证明该算法可收敛至驻点，并在合成数据集与真实数据集上展现出具有竞争力的性能。