MultiFun-DAG: Multivariate Functional Directed Acyclic Graph
arxiv(2024)
摘要
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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