# A Graph Autoencoder Approach to Causal Structure Learning

arXiv: https://arxiv.org/abs/1911.07420 · HTML: https://mlsanity.com/paper/1911.07420/

## Key facts

- Cited by 55 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Nov 2019.

## Built on by (most cited first, 30 of 55)

- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [Deep End-to-end Causal Inference](https://mlsanity.com/paper/2202.02195/) (2022)
- [gCastle: A Python Toolbox for Causal Discovery](https://mlsanity.com/paper/2111.15155/) (2021)
- [Ordering-Based Causal Discovery with Reinforcement Learning](https://mlsanity.com/paper/2105.06631/) (2021)
- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [Learning Neural Causal Models with Active Interventions](https://mlsanity.com/paper/2109.02429/) (2021)
- [A Survey on Causal Discovery Methods for I.I.D. and Time Series Data](https://mlsanity.com/paper/2303.15027/) (2023)
- [Towards Federated Bayesian Network Structure Learning with Continuous Optimization](https://mlsanity.com/paper/2110.09356/) (2021)
- [FedDAG: Federated DAG Structure Learning](https://mlsanity.com/paper/2112.03555/) (2021)
- [Ordering-Based Causal Discovery for Linear and Nonlinear Relations](https://mlsanity.com/paper/2410.05890/) (2024)
- [Recursive Causal Discovery](https://mlsanity.com/paper/2403.09300/) (2024)
- [Deep Causal Learning: Representation, Discovery and Inference](https://mlsanity.com/paper/2211.03374/) (2022)
- [Causality-based CTR Prediction using Graph Neural Networks](https://mlsanity.com/paper/2301.12762/) (2023)
- [Achieving Counterfactual Fairness for Anomaly Detection](https://mlsanity.com/paper/2303.02318/) (2023)
- [On Root Cause Localization and Anomaly Mitigation through Causal Inference](https://mlsanity.com/paper/2212.04031/) (2022)
- [On the Role of Entropy-based Loss for Learning Causal Structures with Continuous Optimization](https://mlsanity.com/paper/2106.02835/) (2021)
- [Boosting Differentiable Causal Discovery via Adaptive Sample Reweighting](https://mlsanity.com/paper/2303.03187/) (2023)
- [Mitigating Prior Errors in Causal Structure Learning: A Resilient Approach via Bayesian Networks](https://mlsanity.com/paper/2306.07032/) (2023)
- [Causal Inference in medicine and in health policy, a summary](https://mlsanity.com/paper/2105.04655/) (2021)
- [Discovering Dynamic Causal Space for DAG Structure Learning](https://mlsanity.com/paper/2306.02822/) (2023)
- [Causal Inference with Latent Variables: Recent Advances and Future Prospectives](https://mlsanity.com/paper/2406.13966/) (2024)
- [The Robustness of Differentiable Causal Discovery in Misspecified Scenarios](https://mlsanity.com/paper/2510.12503/) (2025)
- [Do-Operation Guided Causal Representation Learning with Reduced Supervision Strength](https://mlsanity.com/paper/2206.01802/) (2022)
- [Learning Discrete Directed Acyclic Graphs via Backpropagation](https://mlsanity.com/paper/2210.15353/) (2022)
- [Knowledge Guided Representation Learning and Causal Structure Learning in Soil Science](https://mlsanity.com/paper/2306.09302/) (2023)
- [Shadow Datasets, New challenging datasets for Causal Representation Learning](https://mlsanity.com/paper/2308.05707/) (2023)
- [ACCESS : A Benchmark for Abstract Causal Event Discovery and Reasoning](https://mlsanity.com/paper/2502.08148/) (2025)
- [Scalable Causal Structure Learning: Scoping Review of Traditional and Deep Learning Algorithms and New Opportunities in Biomedicine](https://mlsanity.com/paper/2110.07785/) (2021)
- [Directed Acyclic Graphs With Tears](https://mlsanity.com/paper/2302.02160/) (2023)

## Abstract (arXiv)

Causal structure learning has been a challenging task in the past decades and several mainstream approaches such as constraint- and score-based methods have been studied with theoretical guarantees. Recently, a new approach has transformed the combinatorial structure learning problem into a continuous one and then solved it using gradient-based optimization methods. Following the recent state-of-the-arts, we propose a new gradient-based method to learn causal structures from observational data. The proposed method generalizes the recent gradient-based methods to a graph autoencoder framework that allows nonlinear structural equation models and is easily applicable to vector-valued variables. We demonstrate that on synthetic datasets, our proposed method outperforms other gradient-based methods significantly, especially on large causal graphs. We further investigate the scalability and efficiency of our method, and observe a near linear training time when scaling up the graph size.