MultiFun-DAG: Multivariate Functional Directed Acyclic Graph
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arXiv
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| Hauptverfasser: | , , , , , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911848143519744 |
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| author | Lan, Tian Li, Ziyue Lin, Junpeng Li, Zhishuai Bai, Lei Li, Man Tsung, Fugee Zhao, Rui Zhang, Chen |
| author_facet | Lan, Tian Li, Ziyue Lin, Junpeng Li, Zhishuai Bai, Lei Li, Man Tsung, Fugee Zhao, Rui Zhang, Chen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13836 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | MultiFun-DAG: Multivariate Functional Directed Acyclic Graph Lan, Tian Li, Ziyue Lin, Junpeng Li, Zhishuai Bai, Lei Li, Man Tsung, Fugee Zhao, Rui Zhang, Chen Methodology 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. |
| title | MultiFun-DAG: Multivariate Functional Directed Acyclic Graph |
| topic | Methodology |
| url | https://arxiv.org/abs/2404.13836 |