MultiFun-DAG: Multivariate Functional Directed Acyclic Graph

2024/04/22 by Tian Lan, Lan, Tian, Ziyue Li +15
Computer Science · #Data Management and Algorithms #FOS: Computer and information sciences #Graph Theory and Algorithms #Methodology (stat.ME) #Rough Sets and Fuzzy Logic

paper · pdf · doi:10.48550/arxiv.2404.13836

openalex publication_date 2024/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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