mlsanityData to 7 Oct 2026

Stable Differentiable Causal Discovery

arXiv 2311.10263 ↗First posted 17 Nov 2023cs.LG stat.MEcited by 30

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Abstract (arXiv)

Inferring causal relationships as directed acyclic graphs (DAGs) is an important but challenging problem. Differentiable Causal Discovery (DCD) is a promising approach to this problem, framing the search as a continuous optimization. But existing DCD methods are numerically unstable, with poor performance beyond tens of variables. In this paper, we propose Stable Differentiable Causal Discovery (SDCD), a new method that improves previous DCD methods in two ways: (1) It employs an alternative constraint for acyclicity; this constraint is more stable, both theoretically and empirically, and fast to compute. (2) It uses a training procedure tailored for sparse causal graphs, which are common in real-world scenarios. We first derive SDCD and prove its stability and correctness. We then evaluate it with both observational and interventional data and on both small-scale and large-scale settings. We find that SDCD outperforms existing methods in both convergence speed and accuracy and can scale to thousands of variables. We provide code at https://github.com/azizilab/sdcd.

Key facts. Cited by 30 papers in the map (data through 7 Oct 2026). Builds on 23 of its 49 references that are in the map. First posted on arXiv 17 Nov 2023.

Builds on

23 of 49 references.

References · 23

  1. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 745
  2. 2019DAG-GNN: DAG Structure Learning with Graph Neural Networkscited by 329
  3. 2013Causal Discovery with Continuous Additive Noise Modelscited by 252
  4. 2019Gradient-Based Neural DAG Learningcited by 227
  5. 2020Differentiable Causal Discovery from Interventional Datacited by 218
  6. 2019Learning Sparse Nonparametric DAGscited by 207
  7. 2020On the Role of Sparsity and DAG Constraints for Learning Linear DAGscited by 186
  8. 2013CAM: Causal additive models, high-dimensional order search and penalized regressioncited by 175
  9. 2021Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Gamecited by 159
  10. 2022DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterizationcited by 135
  11. 2022Score matching enables causal discovery of nonlinear additive noise modelscited by 108
  12. 2022Amortized Inference for Causal Structure Learningcited by 89
11 more
  1. 2013High-dimensional learning of linear causal networks via inverse covariance estimationcited by 86
  2. 2021Efficient Neural Causal Discovery without Acyclicity Constraintscited by 82
  3. 2018Characterizing and Learning Equivalence Classes of Causal DAGs under Interventionscited by 76
  4. 2020DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networkscited by 66
  5. 2021DAGs with No Curl: An Efficient DAG Structure Learning Approachcited by 53
  6. 2014Constraint-based Causal Discovery from Multiple Interventions over Overlapping Variable Setscited by 48
  7. 2022Large-Scale Differentiable Causal Discovery of Factor Graphscited by 47
  8. 2019Scaling structural learning with NO-BEARS to infer causal transcriptome networkscited by 39
  9. 2020On the Convergence of Continuous Constrained Optimization for Structure Learningcited by 38
  10. 2023Structure Learning with Continuous Optimization: A Sober Look and Beyondcited by 34
  11. 2023Optimizing NOTEARS Objectives via Topological Swapscited by 17

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 7; 2025: 8; 2026: 15.

30 papers.

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  1. 2025Extremely Greedy Equivalence Searchcited by 8
  2. 2024Deriving Causal Order from Single-Variable Interventions: Guarantees & Algorithmcited by 5
  3. 2024Scalable and Flexible Causal Discovery with an Efficient Test for Adjacencycited by 5
  4. 2024Continuous Bayesian Model Selection for Multivariate Causal Discoverycited by 5
  5. 2026CauScale: Neural Causal Discovery at Scalecited by 5
  6. 2025Since Faithfulness Fails: The Performance Limits of Neural Causal Discoverycited by 4
  7. 2025Causal-Adapter: Taming Text-to-Image Diffusion for Faithful Counterfactual Generationcited by 4
  8. 2026Arrow: A Foundation Model for Causal Discoverycited by 4
  9. 2024Differentiable Causal Discovery For Latent Hierarchical Causal Modelscited by 3
  10. 2024Efficient Differentiable Discovery of Causal Ordercited by 2
  11. 2026Coarse-to-Fine Learning of Dynamic Causal Structurescited by 2
  12. 2024Revisiting Differentiable Structure Learning: Inconsistency of ℓ1 Penalty and Beyondcited by 1
18 more
  1. 2025Amortized Causal Discovery with Prior-Fitted Networkscited by 1
  2. 2024Kernel-Based Differentiable Learning of Non-Parametric Directed Acyclic Graphical Modelscited by 0
  3. 2025Differentiable Structure Learning and Causal Discovery for General Binary Datacited by 0
  4. 2025Large-Scale Bayesian Causal Discovery with Interventional Datacited by 0
  5. 2025Theoretical Guarantees for Causal Discovery on Large Random Graphscited by 0
  6. 2025DAG Learning from Zero-Inflated Count Data Using Continuous Optimizationcited by 0
  7. 2026SC3D: Dynamic and Differentiable Causal Discovery for Temporal and Instantaneous Graphscited by 0
  8. 2026Neural Autoregressive Flows for Markov Boundary Learningcited by 0
  9. 2026Smoothing the Landscape: Causal Structure Learning via Diffusion Denoising Objectivescited by 0
  10. 2026When Does Gene Regulatory Network Inference Break? A Controlled Diagnostic Study of Causal and Correlational Methods on Single-Cell Datacited by 0
  11. 2026PACER: Acyclic Causal Discovery from Large-Scale Interventional Datacited by 0
  12. 2026KG-SoftMAP: Soft Knowledge-Graph Priors for Bayesian Network Structure Learning from Sparse Discrete Datacited by 0
  13. 2026Unsupervised Causal Abstractions Discoverycited by 0
  14. 2026Amortized Bayesian Causal Discovery of Extended Factor Graphscited by 0
  15. 2026Support Selection Beyond Smooth DAG Exactness: Completion Geometry,Score Margins, and Selective Certificatescited by 0
  16. 2026Guide, Not Bind: Why Defeasible Priors Fail in Augmented Lagrangian Causal Discoverycited by 0
  17. 2026CausalArena: Benchmarking Causal Discovery in the Foundation Model Eracited by 0
  18. 2026Demistifying Data and Simulator Assumptions in Supervised Causal Discoverycited by 0