# On Low Rank Directed Acyclic Graphs and Causal Structure Learning

arXiv: https://arxiv.org/abs/2006.05691 · HTML: https://mlsanity.com/paper/2006.05691/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2020.

## Built on by (most cited first, 23 of 23)

- [gCastle: A Python Toolbox for Causal Discovery](https://mlsanity.com/paper/2111.15155/) (2021)
- [Large-Scale Differentiable Causal Discovery of Factor Graphs](https://mlsanity.com/paper/2206.07824/) (2022)
- [FedDAG: Federated DAG Structure Learning](https://mlsanity.com/paper/2112.03555/) (2021)
- [Graph Neural Flows for Unveiling Systemic Interactions Among Irregularly Sampled Time Series](https://mlsanity.com/paper/2410.14030/) (2024)
- [Constraint-Free Structure Learning with Smooth Acyclic Orientations](https://mlsanity.com/paper/2309.08406/) (2023)
- [Evaluation of Induced Expert Knowledge in Causal Structure Learning by NOTEARS](https://mlsanity.com/paper/2301.01817/) (2023)
- [Extremely Greedy Equivalence Search](https://mlsanity.com/paper/2502.19551/) (2025)
- [Granger Causal Chain Discovery for Sepsis-Associated Derangements via Continuous-Time Hawkes Processes](https://mlsanity.com/paper/2209.04480/) (2022)
- [Interpretable Neural ODEs for Gene Regulatory Network Discovery under Perturbations](https://mlsanity.com/paper/2501.02409/) (2025)
- [From graphs to DAGs: a low-complexity model and a scalable algorithm](https://mlsanity.com/paper/2204.04644/) (2022)
- [Weakly-supervised causal discovery based on fuzzy knowledge and complex data complementarity](https://mlsanity.com/paper/2405.08699/) (2024)
- [Robust Causal Discovery under Imperfect Structural Constraints](https://mlsanity.com/paper/2511.06790/) (2025)
- [Causal Graph Discovery from Self and Mutually Exciting Time Series](https://mlsanity.com/paper/2301.11197/) (2023)
- [Towards Human-like Perception: Learning Structural Causal Model in Heterogeneous Graph](https://mlsanity.com/paper/2312.05757/) (2023)
- [Causal Discovery via Bayesian Optimization](https://mlsanity.com/paper/2501.14997/) (2025)
- [Towards Identifiability of Interventional Stochastic Differential Equations](https://mlsanity.com/paper/2505.15987/) (2025)
- [Unsupervised Causal Abstractions Discovery](https://mlsanity.com/paper/2606.19594/) (2026)
- [Causal Graph Discovery from Self and Mutually Exciting Time Series](https://mlsanity.com/paper/2106.02600/) (2021)
- [Causal Structural Learning from Time Series: A Convex Optimization Approach](https://mlsanity.com/paper/2301.11336/) (2023)
- [Causality-Induced Positional Encoding for Transformer-Based Representation Learning of Non-Sequential Features](https://mlsanity.com/paper/2509.16629/) (2025)
- [Efficient Causal Structure Learning via Modular Subgraph Integration](https://mlsanity.com/paper/2601.21014/) (2026)
- [Time Series Gaussian Chain Graph Models](https://mlsanity.com/paper/2604.07018/) (2026)
- [PACER: Acyclic Causal Discovery from Large-Scale Interventional Data](https://mlsanity.com/paper/2605.15353/) (2026)

## Abstract (arXiv)

Despite several advances in recent years, learning causal structures represented by directed acyclic graphs (DAGs) remains a challenging task in high dimensional settings when the graphs to be learned are not sparse. In this paper, we propose to exploit a low rank assumption regarding the (weighted) adjacency matrix of a DAG causal model to help address this problem. We utilize existing low rank techniques to adapt causal structure learning methods to take advantage of this assumption and establish several useful results relating interpretable graphical conditions to the low rank assumption. Specifically, we show that the maximum rank is highly related to hubs, suggesting that scale-free networks, which are frequently encountered in practice, tend to be low rank. Our experiments demonstrate the utility of the low rank adaptations for a variety of data models, especially with relatively large and dense graphs. Moreover, with a validation procedure, the adaptations maintain a superior or comparable performance even when graphs are not restricted to be low rank.