mlsanityData to 14 Oct 2026

Efficient Neural Causal Discovery without Acyclicity Constraints

arXiv 2107.10483 ↗First posted 22 Jul 2021cs.LG cs.AI stat.MLcited by 82

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Abstract (arXiv)

Learning the structure of a causal graphical model using both observational and interventional data is a fundamental problem in many scientific fields. A promising direction is continuous optimization for score-based methods, which, however, require constrained optimization to enforce acyclicity or lack convergence guarantees. In this paper, we present ENCO, an efficient structure learning method for directed, acyclic causal graphs leveraging observational and interventional data. ENCO formulates the graph search as an optimization of independent edge likelihoods, with the edge orientation being modeled as a separate parameter. Consequently, we can provide convergence guarantees of ENCO under mild conditions without constraining the score function with respect to acyclicity. In experiments, we show that ENCO can efficiently recover graphs with hundreds of nodes, an order of magnitude larger than what was previously possible, while handling deterministic variables and latent confounders.

Key facts. Cited by 82 papers in the map (data through 14 Oct 2026). Builds on 26 of its 71 references that are in the map. First posted on arXiv 22 Jul 2021.

Builds on

26 of 71 references.

References · 26

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  9. 2020Differentiable Causal Discovery from Interventional Datacited by 218
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14 more
  1. 2020On the Role of Sparsity and DAG Constraints for Learning Linear DAGscited by 191
  2. 2019A Meta-Transfer Objective for Learning to Disentangle Causal Mechanismscited by 158
  3. 2019Causal Discovery with Reinforcement Learningcited by 145
  4. 2017Invariant Causal Prediction for Nonlinear Modelscited by 140
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  6. 2017Permutation-based Causal Inference Algorithms with Interventionscited by 78
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  8. 2018Variational Autoencoder with Arbitrary Conditioningcited by 68
  9. 2019Causal Discovery with General Non-Linear Relationships Using Non-Linear ICAcited by 58
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 1; 2022: 15; 2023: 15; 2024: 22; 2025: 16; 2026: 13.

82 papers.

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  1. 2022Weakly supervised causal representation learningcited by 140
  2. 2022CITRIS: Causal Identifiability from Temporal Intervened Sequencescited by 133
  3. 2022Deep End-to-end Causal Inferencecited by 95
  4. 2022Learning to Induce Causal Structurecited by 68
  5. 2022Causal Representation Learning for Instantaneous and Temporal Effects in Interactive Systemscited by 51
  6. 2022Large-Scale Differentiable Causal Discovery of Factor Graphscited by 47
  7. 2021Learning Neural Causal Models with Active Interventionscited by 40
  8. 2023BISCUIT: Causal Representation Learning from Binary Interactionscited by 38
  9. 2023CausalTime: Realistically Generated Time-series for Benchmarking of Causal Discoverycited by 36
  10. 2022Active Bayesian Causal Inferencecited by 35
  11. 2023A Survey on Causal Discovery Methods for I.I.D. and Time Series Datacited by 35
  12. 2023CUTS: Neural Causal Discovery from Irregular Time-Series Datacited by 33
38 more
  1. 2023Stable Differentiable Causal Discoverycited by 31
  2. 2023From Identifiable Causal Representations to Controllable Counterfactual Generation: A Survey on Causal Generative Modelingcited by 22
  3. 2024Sample, estimate, aggregate: A recipe for causal discovery foundation modelscited by 21
  4. 2022Deep Learning of Causal Structures in High Dimensionscited by 20
  5. 2022Variational Causal Dynamics: Discovering Modular World Models from Interventionscited by 16
  6. 2023Causal Reasoning in the Presence of Latent Confounders via Neural ADMG Learningcited by 15
  7. 2024Federated Causal Discovery from Heterogeneous Datacited by 15
  8. 2023CoLiDE: Concomitant Linear DAG Estimationcited by 13
  9. 2024Predictive, scalable and interpretable knowledge tracing on structured domainscited by 13
  10. 2022A Meta-Reinforcement Learning Algorithm for Causal Discoverycited by 11
  11. 2022Deep Causal Learning: Representation, Discovery and Inferencecited by 11
  12. 2024Demystifying amortized causal discovery with transformerscited by 11
  13. 2025Can Large Language Models Help Experimental Design for Causal Discovery?cited by 11
  14. 2025Learning Interactive World Model for Object-Centric Reinforcement Learningcited by 11
  15. 2023Constraint-Free Structure Learning with Smooth Acyclic Orientationscited by 10
  16. 2024Score matching through the roof: linear, nonlinear, and latent variables causal discoverycited by 10
  17. 2023DAG Learning on the Permutahedroncited by 9
  18. 2022On the Generalization and Adaption Performance of Causal Modelscited by 8
  19. 2024LLM4GRN: Discovering Causal Gene Regulatory Networks with LLMs -- Evaluation through Synthetic Data Generationcited by 7
  20. 2024CORE: Towards Scalable and Efficient Causal Discovery with Reinforcement Learningcited by 6
  21. 2024Continuous Bayesian Model Selection for Multivariate Causal Discoverycited by 6
  22. 2026CauScale: Neural Causal Discovery at Scalecited by 6
  23. 2022Trust Your nabla: Gradient-based Intervention Targeting for Causal Discoverycited by 5
  24. 2023Boosting Differentiable Causal Discovery via Adaptive Sample Reweightingcited by 5
  25. 2023Discovering Dynamic Causal Space for DAG Structure Learningcited by 4
  26. 2023Shortcuts for causal discovery of nonlinear models by score matchingcited by 4
  27. 2024Permutation-based Inference for Variational Learning of Directed Acyclic Graphscited by 4
  28. 2024Knockout: A simple way to handle missing inputscited by 4
  29. 2025Since Faithfulness Fails: The Performance Limits of Neural Causal Discoverycited by 4
  30. 2022Differentiable Invariant Causal Discoverycited by 3
  31. 2023DiscoGen: Learning to Discover Gene Regulatory Networkscited by 3
  32. 2024Simulation-based Benchmarking for Causal Structure Learning in Gene Perturbation Experimentscited by 3
  33. 2024Reinforcement Learning for Causal Discovery without Acyclicity Constraintscited by 3
  34. 2024CAnDOIT: Causal Discovery with Observational and Interventional Data from Time-Seriescited by 3
  35. 2025Learning Identifiable Structures Helps Avoid Bias in DNN-based Supervised Causal Learningcited by 3
  36. 2025IGDA: Interactive Graph Discovery through Large Language Model Agentscited by 3
  37. 2025Revealing Multimodal Causality with Large Language Modelscited by 3
  38. 2025From Pixels to Factors: Learning Independently Controllable State Variables for Reinforcement Learningcited by 3

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