Structural Discovery with Partial Ordering Information for Time-Dependent Data with Convergence Guarantees

Jiahe Lin; Huitian Lei; George Michailidis

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arXiv · 2311.15434

Structural Discovery with Partial Ordering Information for Time-Dependent Data with Convergence Guarantees

Jiahe Lin·Huitian Lei·George Michailidis

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Abstract

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.

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Jiahe Lin, Huitian Lei, George Michailidis. 2023-11-26. Structural Discovery with Partial Ordering Information for Time-Dependent Data with Convergence Guarantees. https://arxiv.org/abs/2311.15434

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