# MM-DAG: Multi-task DAG Learning for Multi-modal Data -- with Application for Traffic Congestion Analysis

arXiv: https://arxiv.org/abs/2306.02831 · HTML: https://mlsanity.com/paper/2306.02831/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 53 references that are in the map.
- First posted on arXiv 5 Jun 2023.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Survey on Multi-Task Learning](https://mlsanity.com/paper/1707.08114/) (2017)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Differentiable Causal Discovery Under Unmeasured Confounding](https://mlsanity.com/paper/2010.06978/) (2020)
- [High-dimensional consistency in score-based and hybrid structure learning](https://mlsanity.com/paper/1507.02608/) (2015)
- [Metrics for Graph Comparison: A Practitioner's Guide](https://mlsanity.com/paper/1904.07414/) (2019)
- [On the Convergence of Continuous Constrained Optimization for Structure Learning](https://mlsanity.com/paper/2011.11150/) (2020)
- [Jointly Contrastive Representation Learning on Road Network and Trajectory](https://mlsanity.com/paper/2209.06389/) (2022)
- [Tensor Completion for Weakly-dependent Data on Graph for Metro Passenger Flow Prediction](https://mlsanity.com/paper/1912.05693/) (2019)
- [Deep Learning for Functional Data Analysis with Adaptive Basis Layers](https://mlsanity.com/paper/2106.10414/) (2021)
- [FedDAG: Federated DAG Structure Learning](https://mlsanity.com/paper/2112.03555/) (2021)
- [Long-Short Term Spatiotemporal Tensor Prediction for Passenger Flow Profile](https://mlsanity.com/paper/2004.11022/) (2020)
- [Multi-task Learning of Order-Consistent Causal Graphs](https://mlsanity.com/paper/2111.02545/) (2021)
- [Exact Estimation of Multiple Directed Acyclic Graphs](https://mlsanity.com/paper/1404.1238/) (2014)
- [An Overview of General Performance Metrics of Binary Classifier Systems](https://mlsanity.com/paper/1410.5330/) (2014)
- [Distributed Classification of Urban Congestion Using VANET](https://mlsanity.com/paper/1904.12685/) (2019)
- [Cooperative Evaluation of the Cause of Urban Traffic Congestion via Connected Vehicles](https://mlsanity.com/paper/1905.01993/) (2019)
- [Bayesian Discovery of Multiple Bayesian Networks via Transfer Learning](https://mlsanity.com/paper/1307.2312/) (2013)

## Built on by (most cited first, 13 of 13)

- [Dynamic Causal Graph Convolutional Network for Traffic Prediction](https://mlsanity.com/paper/2306.07019/) (2023)
- [Correlated Time Series Self-Supervised Representation Learning via Spatiotemporal Bootstrapping](https://mlsanity.com/paper/2306.06994/) (2023)
- [LEMMA-RCA: A Large Multi-modal Multi-domain Dataset for Root Cause Analysis](https://mlsanity.com/paper/2406.05375/) (2024)
- [Grid and Road Expressions Are Complementary for Trajectory Representation Learning](https://mlsanity.com/paper/2411.14768/) (2024)
- [Adaptive Hierarchical SpatioTemporal Network for Traffic Forecasting](https://mlsanity.com/paper/2306.09386/) (2023)
- [Tensor Dirichlet Process Multinomial Mixture Model for Passenger Trajectory Clustering](https://mlsanity.com/paper/2306.13794/) (2023)
- [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)
- [Online Multi-modal Root Cause Identification in Microservice Systems](https://mlsanity.com/paper/2410.10021/) (2024)
- [Data-Driven Optimization of EV Charging Station Placement Using Causal Discovery](https://mlsanity.com/paper/2503.17055/) (2025)
- [Function-on-Function Bayesian Optimization](https://mlsanity.com/paper/2511.12783/) (2025)
- [Transformer-based Drum-level Prediction in a Boiler Plant with Delayed Relations among Multivariates](https://mlsanity.com/paper/2407.11180/) (2024)
- [FAME: Adaptive Functional Attention with Expert Routing for Function-on-Function Regression](https://mlsanity.com/paper/2510.00621/) (2025)

## Abstract (arXiv)

This paper proposes to learn Multi-task, Multi-modal Direct Acyclic Graphs (MM-DAGs), which are commonly observed in complex systems, e.g., traffic, manufacturing, and weather systems, whose variables are multi-modal with scalars, vectors, and functions. This paper takes the traffic congestion analysis as a concrete case, where a traffic intersection is usually regarded as a DAG. In a road network of multiple intersections, different intersections can only have some overlapping and distinct variables observed. For example, a signalized intersection has traffic light-related variables, whereas unsignalized ones do not. This encourages the multi-task design: with each DAG as a task, the MM-DAG tries to learn the multiple DAGs jointly so that their consensus and consistency are maximized. To this end, we innovatively propose a multi-modal regression for linear causal relationship description of different variables. Then we develop a novel Causality Difference (CD) measure and its differentiable approximator. Compared with existing SOTA measures, CD can penalize the causal structural difference among DAGs with distinct nodes and can better consider the uncertainty of causal orders. We rigidly prove our design's topological interpretation and consistency properties. We conduct thorough simulations and one case study to show the effectiveness of our MM-DAG. The code is available under https://github.com/Lantian72/MM-DAG