mlsanityData to 7 Oct 2026

Differentiable Causal Discovery Under Unmeasured Confounding

arXiv 2010.06978 ↗First posted 14 Oct 2020cs.LG stat.MLcited by 56

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Abstract (arXiv)

The data drawn from biological, economic, and social systems are often confounded due to the presence of unmeasured variables. Prior work in causal discovery has focused on discrete search procedures for selecting acyclic directed mixed graphs (ADMGs), specifically ancestral ADMGs, that encode ordinary conditional independence constraints among the observed variables of the system. However, confounded systems also exhibit more general equality restrictions that cannot be represented via these graphs, placing a limit on the kinds of structures that can be learned using ancestral ADMGs. In this work, we derive differentiable algebraic constraints that fully characterize the space of ancestral ADMGs, as well as more general classes of ADMGs, arid ADMGs and bow-free ADMGs, that capture all equality restrictions on the observed variables. We use these constraints to cast causal discovery as a continuous optimization problem and design differentiable procedures to find the best fitting ADMG when the data comes from a confounded linear system of equations with correlated errors. We demonstrate the efficacy of our method through simulations and application to a protein expression dataset. Code implementing our methods is open-source and publicly available at https://gitlab.com/rbhatta8/dcd and will be incorporated into the Ananke package.

Key facts. Cited by 56 papers in the map (data through 7 Oct 2026). First posted on arXiv 14 Oct 2020.

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Citing papers per year: 2021: 11; 2022: 11; 2023: 7; 2024: 10; 2025: 11; 2026: 6.

56 papers.

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  1. 2021D'ya like DAGs? A Survey on Structure Learning and Causal Discoverycited by 209
  2. 2021Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Gamecited by 159
  3. 2022DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterizationcited by 135
  4. 2022Deep End-to-end Causal Inferencecited by 93
  5. 2022Amortized Inference for Causal Structure Learningcited by 89
  6. 2021gCastle: A Python Toolbox for Causal Discoverycited by 60
  7. 2021Unsuitability of NOTEARS for Causal Graph Discoverycited by 46
  8. 2022Causal Structure Learning: a Combinatorial Perspectivecited by 46
  9. 2023Structure Learning with Continuous Optimization: A Sober Look and Beyondcited by 34
  10. 2021Towards Federated Bayesian Network Structure Learning with Continuous Optimizationcited by 31
  11. 2021CausalCity: Complex Simulations with Agency for Causal Discovery and Reasoningcited by 23
  12. 2022Truncated Matrix Power Iteration for Differentiable DAG Learningcited by 23
38 more
  1. 2022MissDAG: Causal Discovery in the Presence of Missing Data with Continuous Additive Noise Modelscited by 21
  2. 2021DoWhy: Addressing Challenges in Expressing and Validating Causal Assumptionscited by 20
  3. 2021FedDAG: Federated DAG Structure Learningcited by 17
  4. 2024Causal Graph Discovery with Retrieval-Augmented Generation based Large Language Modelscited by 16
  5. 2023Causal Reasoning in the Presence of Latent Confounders via Neural ADMG Learningcited by 15
  6. 2021Integer Programming for Causal Structure Learning in the Presence of Latent Variablescited by 14
  7. 2023MM-DAG: Multi-task DAG Learning for Multi-modal Data -- with Application for Traffic Congestion Analysiscited by 13
  8. 2021Context-Specific Causal Discovery for Categorical Data Using Staged Treescited by 10
  9. 2022Valid Inference After Causal Discoverycited by 10
  10. 2022On Testability of the Front-Door Model via Verma Constraintscited by 8
  11. 2023Expert-Aided Causal Discovery of Ancestral Graphscited by 8
  12. 2024Scalable Differentiable Causal Discovery in the Presence of Latent Confounders with Skeleton Posterior (Extended Version)cited by 6
  13. 2025Causal Additive Models with Unobserved Causal Paths and Backdoor Pathscited by 5
  14. 2023Discovering Dynamic Causal Space for DAG Structure Learningcited by 4
  15. 2025Differentiable Cyclic Causal Discovery Under Unmeasured Confounderscited by 4
  16. 2021Entropic Inequality Constraints from e-separation Relations in Directed Acyclic Graphs with Hidden Variablescited by 3
  17. 2022Differentiable Invariant Causal Discoverycited by 3
  18. 2022On the Sparse DAG Structure Learning Based on Adaptive Lassocited by 3
  19. 2024Detecting and Measuring Confounding Using Causal Mechanism Shiftscited by 3
  20. 2024psiDAG: Projected Stochastic Approximation Iteration for DAG Structure Learningcited by 3
  21. 2024Differentiable Causal Discovery For Latent Hierarchical Causal Modelscited by 3
  22. 2026FoundCause: Causal Discovery with Latent Confounders from Observational Datacited by 3
  23. 2023CTP:A Causal Interpretable Model for Non-Communicable Disease Progression Predictioncited by 2
  24. 2024PORCA: Root Cause Analysis with Partially Observed Datacited by 2
  25. 2025Efficient Latent Variable Causal Discovery: Combining Score Search and Targeted Testingcited by 2
  26. 2025Robust Causal Discovery under Imperfect Structural Constraintscited by 2
  27. 2026Score-Based Causal Discovery of Latent Variable Causal Modelscited by 2
  28. 2023A Review and Roadmap of Deep Causal Model from Different Causal Structures and Representationscited by 1
  29. 2024Revisiting Differentiable Structure Learning: Inconsistency of ℓ1 Penalty and Beyondcited by 1
  30. 2024MissNODAG: Differentiable Cyclic Causal Graph Learning from Incomplete Datacited by 1
  31. 2024Score-matching-based Structure Learning for Temporal Data on Networkscited by 1
  32. 2025ExMAG: Learning of Maximally Ancestral Graphscited by 1
  33. 2025dcFCI: Robust Causal Discovery Under Latent Confounding, Unfaithfulness, and Mixed Datacited by 1
  34. 2025Score-based Greedy Search for Structure Identification of Partially Observed Linear Causal Modelscited by 1
  35. 2026Robust Weighted Triangulation of Causal Effects Under Model Uncertaintycited by 1
  36. 2022Differentiable and Transportable Structure Learningcited by 0
  37. 2024Boosting Causal Additive Modelscited by 0
  38. 2025Addressing pitfalls in implicit unobserved confounding synthesis using explicit block hierarchical ancestral samplingcited by 0

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