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arXiv · 2404.13836

MultiFun-DAG: Multivariate Functional Directed Acyclic Graph

Tian Lan·Ziyue Li·Junpeng Lin·Zhishuai Li·Lei Bai·Man Li·Fugee Tsung·Rui Zhao·Chen Zhang
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Abstract

Directed Acyclic Graphical (DAG) models efficiently formulate causal relationships in complex systems. Traditional DAGs assume nodes to be scalar variables, characterizing complex systems under a facile and oversimplified form. This paper considers that nodes can be multivariate functional data and thus proposes a multivariate functional DAG (MultiFun-DAG). It constructs a hidden bilinear multivariate function-to-function regression to describe the causal relationships between different nodes. Then an Expectation-Maximum algorithm is used to learn the graph structure as a score-based algorithm with acyclic constraints. Theoretical properties are diligently derived. Prudent numerical studies and a case study from urban traffic congestion analysis are conducted to show MultiFun-DAG's effectiveness.

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Tian Lan, Ziyue Li, Junpeng Lin, Zhishuai Li, Lei Bai, Man Li, Fugee Tsung, Rui Zhao, Chen Zhang. 2024-04-22. MultiFun-DAG: Multivariate Functional Directed Acyclic Graph. https://arxiv.org/abs/2404.13836

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