# MultiFun-DAG: Multivariate Functional Directed Acyclic Graph

arXiv: https://arxiv.org/abs/2404.13836 · HTML: https://mlsanity.com/paper/2404.13836/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Apr 2024.

## Built on by (most cited first, 4 of 4)

- [TraffiDent: A Dataset for Understanding the Interplay Between Traffic Dynamics and Incidents](https://mlsanity.com/paper/2407.11477/) (2024)
- [Deep Causal Learning to Explain and Quantify The Geo-Tension's Impact on Natural Gas Market](https://mlsanity.com/paper/2407.10878/) (2024)
- [Data-Driven Optimization of EV Charging Station Placement Using Causal Discovery](https://mlsanity.com/paper/2503.17055/) (2025)
- [Transformer-based Drum-level Prediction in a Boiler Plant with Delayed Relations among Multivariates](https://mlsanity.com/paper/2407.11180/) (2024)

## Abstract (arXiv)

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.