# Directed Acyclic Graph Structure Learning from Dynamic Graphs

arXiv: https://arxiv.org/abs/2211.17029 · HTML: https://mlsanity.com/paper/2211.17029/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 45 references that are in the map.
- First posted on arXiv 30 Nov 2022.

## Builds on (most cited first, 16 of 16)

- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Temporal Graph Networks for Deep Learning on Dynamic Graphs](https://mlsanity.com/paper/2006.10637/) (2020)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [High-dimensional learning of linear causal networks via inverse covariance estimation](https://mlsanity.com/paper/1311.3492/) (2013)
- [Debiasing Graph Neural Networks via Learning Disentangled Causal Substructure](https://mlsanity.com/paper/2209.14107/) (2022)
- [Generalizing Graph Neural Networks on Out-Of-Distribution Graphs](https://mlsanity.com/paper/2111.10657/) (2021)
- [Learning Gaussian Networks](https://mlsanity.com/paper/1302.6808/) (2013)
- [Debiased Graph Neural Networks with Agnostic Label Selection Bias](https://mlsanity.com/paper/2201.07708/) (2022)
- [A Sound and Complete Algorithm for Learning Causal Models from Relational Data](https://mlsanity.com/paper/1309.6843/) (2013)
- [Learning Directed Acyclic Graphs with Penalized Neighbourhood Regression](https://mlsanity.com/paper/1511.08963/) (2015)

## Built on by (most cited first, 5 of 5)

- [A Comprehensive Survey of Dynamic Graph Neural Networks: Models, Frameworks, Benchmarks, Experiments and Challenges](https://mlsanity.com/paper/2405.00476/) (2024)
- [Graph Contrastive Invariant Learning from the Causal Perspective](https://mlsanity.com/paper/2401.12564/) (2024)
- [Dynamic Causal Structure Discovery and Causal Effect Estimation](https://mlsanity.com/paper/2501.06534/) (2025)
- [LOCAL: Learning with Orientation Matrix to Infer Causal Structure from Time Series Data](https://mlsanity.com/paper/2410.19464/) (2024)
- [Score-matching-based Structure Learning for Temporal Data on Networks](https://mlsanity.com/paper/2412.07469/) (2024)

## Abstract (arXiv)

Estimating the structure of directed acyclic graphs (DAGs) of features (variables) plays a vital role in revealing the latent data generation process and providing causal insights in various applications. Although there have been many studies on structure learning with various types of data, the structure learning on the dynamic graph has not been explored yet, and thus we study the learning problem of node feature generation mechanism on such ubiquitous dynamic graph data. In a dynamic graph, we propose to simultaneously estimate contemporaneous relationships and time-lagged interaction relationships between the node features. These two kinds of relationships form a DAG, which could effectively characterize the feature generation process in a concise way. To learn such a DAG, we cast the learning problem as a continuous score-based optimization problem, which consists of a differentiable score function to measure the validity of the learned DAGs and a smooth acyclicity constraint to ensure the acyclicity of the learned DAGs. These two components are translated into an unconstraint augmented Lagrangian objective which could be minimized by mature continuous optimization techniques. The resulting algorithm, named GraphNOTEARS, outperforms baselines on simulated data across a wide range of settings that may encounter in real-world applications. We also apply the proposed approach on two dynamic graphs constructed from the real-world Yelp dataset, demonstrating our method could learn the connections between node features, which conforms with the domain knowledge.