# Masked Gradient-Based Causal Structure Learning

arXiv: https://arxiv.org/abs/1910.08527 · HTML: https://mlsanity.com/paper/1910.08527/

## Key facts

- Cited by 89 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Oct 2019.

## Built on by (most cited first, 30 of 89)

- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA](https://mlsanity.com/paper/2107.10098/) (2021)
- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [Diffusion Models for Causal Discovery via Topological Ordering](https://mlsanity.com/paper/2210.06201/) (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)
- [DAGs with No Curl: An Efficient DAG Structure Learning Approach](https://mlsanity.com/paper/2106.07197/) (2021)
- [Causal Representation Learning for Instantaneous and Temporal Effects in Interactive Systems](https://mlsanity.com/paper/2206.06169/) (2022)
- [Unsuitability of NOTEARS for Causal Graph Discovery](https://mlsanity.com/paper/2104.05441/) (2021)
- [Differentiable DAG Sampling](https://mlsanity.com/paper/2203.08509/) (2022)
- [Large-Scale Differentiable Causal Discovery of Factor Graphs](https://mlsanity.com/paper/2206.07824/) (2022)
- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [Structure Learning with Continuous Optimization: A Sober Look and Beyond](https://mlsanity.com/paper/2304.02146/) (2023)
- [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)
- [Improving Multi-Task Generalization via Regularizing Spurious Correlation](https://mlsanity.com/paper/2205.09797/) (2022)
- [Truncated Matrix Power Iteration for Differentiable DAG Learning](https://mlsanity.com/paper/2208.14571/) (2022)
- [MissDAG: Causal Discovery in the Presence of Missing Data with Continuous Additive Noise Models](https://mlsanity.com/paper/2205.13869/) (2022)
- [From Identifiable Causal Representations to Controllable Counterfactual Generation: A Survey on Causal Generative Modeling](https://mlsanity.com/paper/2310.11011/) (2023)
- [Differentiable Causal Discovery Under Latent Interventions](https://mlsanity.com/paper/2203.02336/) (2022)
- [NODAGS-Flow: Nonlinear Cyclic Causal Structure Learning](https://mlsanity.com/paper/2301.01849/) (2023)
- [FedDAG: Federated DAG Structure Learning](https://mlsanity.com/paper/2112.03555/) (2021)
- [DeepRicci: Self-supervised Graph Structure-Feature Co-Refinement for Alleviating Over-squashing](https://mlsanity.com/paper/2401.12780/) (2024)
- [Identifiable Exchangeable Mechanisms for Causal Structure and Representation Learning](https://mlsanity.com/paper/2406.14302/) (2024)
- [Learning Causally Disentangled Representations via the Principle of Independent Causal Mechanisms](https://mlsanity.com/paper/2306.01213/) (2023)
- [RDGSL: Dynamic Graph Representation Learning with Structure Learning](https://mlsanity.com/paper/2309.02025/) (2023)
- [RealTCD: Temporal Causal Discovery from Interventional Data with Large Language Model](https://mlsanity.com/paper/2404.14786/) (2024)
- [Guided Hybrid Quantization for Object detection in Multimodal Remote Sensing Imagery via One-to-one Self-teaching](https://mlsanity.com/paper/2301.00131/) (2022)
- [ML4C: Seeing Causality Through Latent Vicinity](https://mlsanity.com/paper/2110.00637/) (2021)
- [Towards Privacy-Aware Causal Structure Learning in Federated Setting](https://mlsanity.com/paper/2211.06919/) (2022)

## Abstract (arXiv)

This paper studies the problem of learning causal structures from observational data. We reformulate the Structural Equation Model (SEM) with additive noises in a form parameterized by binary graph adjacency matrix and show that, if the original SEM is identifiable, then the binary adjacency matrix can be identified up to super-graphs of the true causal graph under mild conditions. We then utilize the reformulated SEM to develop a causal structure learning method that can be efficiently trained using gradient-based optimization, by leveraging a smooth characterization on acyclicity and the Gumbel-Softmax approach to approximate the binary adjacency matrix. It is found that the obtained entries are typically near zero or one and can be easily thresholded to identify the edges. We conduct experiments on synthetic and real datasets to validate the effectiveness of the proposed method, and show that it readily includes different smooth model functions and achieves a much improved performance on most datasets considered.