MultiFun-DAG: Multivariate Functional Directed Acyclic Graph

TL;DR

This paper introduces MultiFun-DAG, a novel causal modeling framework for multivariate functional data using a bilinear regression approach and an E-M algorithm, with theoretical guarantees and practical applications.

Contribution

It extends traditional DAG models to multivariate functional data, proposing a new regression-based structure learning method with proven properties.

Findings

Effective in modeling complex causal relationships

Demonstrates strong performance in numerical studies

Successfully applied to urban traffic congestion analysis

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.