Structural Discovery with Partial Ordering Information for Time-Dependent Data with Convergence Guarantees
本文提出一种算法，在变量间存在超前滞后关系时，利用部分排序信息约束有向无环图，求解高维线性结构方程模型，并证明算法收敛到稳定点。
Structural discovery among 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 article 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 datasets. Supplementary materials for this article are available online.