mlsanityData to 14 Oct 2026

Large-Scale Differentiable Causal Discovery of Factor Graphs

arXiv 2206.07824 ↗First posted 15 Jun 2022stat.ML cs.LG q-bio.GNcited by 47

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Abstract (arXiv)

A common theme in causal inference is learning causal relationships between observed variables, also known as causal discovery. This is usually a daunting task, given the large number of candidate causal graphs and the combinatorial nature of the search space. Perhaps for this reason, most research has so far focused on relatively small causal graphs, with up to hundreds of nodes. However, recent advances in fields like biology enable generating experimental data sets with thousands of interventions followed by rich profiling of thousands of variables, raising the opportunity and urgent need for large causal graph models. Here, we introduce the notion of factor directed acyclic graphs (f-DAGs) as a way to restrict the search space to non-linear low-rank causal interaction models. Combining this novel structural assumption with recent advances that bridge the gap between causal discovery and continuous optimization, we achieve causal discovery on thousands of variables. Additionally, as a model for the impact of statistical noise on this estimation procedure, we study a model of edge perturbations of the f-DAG skeleton based on random graphs and quantify the effect of such perturbations on the f-DAG rank. This theoretical analysis suggests that the set of candidate f-DAGs is much smaller than the whole DAG space and thus may be more suitable as a search space in the high-dimensional regime where the underlying skeleton is hard to assess. We propose Differentiable Causal Discovery of Factor Graphs (DCD-FG), a scalable implementation of -DAG constrained causal discovery for high-dimensional interventional data. DCD-FG uses a Gaussian non-linear low-rank structural equation model and shows significant improvements compared to state-of-the-art methods in both simulations as well as a recent large-scale single-cell RNA sequencing data set with hundreds of genetic interventions.

Key facts. Cited by 47 papers in the map (data through 14 Oct 2026). Builds on 27 of its 67 references that are in the map. First posted on arXiv 15 Jun 2022.

Builds on

27 of 67 references.

References · 27

  1. 2016The Concrete Distribution: A Continuous Relaxation of Discrete Random Variablescited by 1,148
  2. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 752
  3. 2019DAG-GNN: DAG Structure Learning with Graph Neural Networkscited by 331
  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 191
  8. 2021Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Gamecited by 161
  9. 2021DiBS: Differentiable Bayesian Structure Learningcited by 106
  10. 2019Masked Gradient-Based Causal Structure Learningcited by 89
  11. 2021Efficient Neural Causal Discovery without Acyclicity Constraintscited by 82
  12. 2017Permutation-based Causal Inference Algorithms with Interventionscited by 78
15 more
  1. 2018Characterizing and Learning Equivalence Classes of Causal DAGs under Interventionscited by 76
  2. 2019Permutation-Based Causal Structure Learning with Unknown Intervention Targetscited by 69
  3. 2019Causal Discovery Toolbox: Uncover causal relationships in Pythoncited by 49
  4. 2018Structural Agnostic Modeling: Adversarial Learning of Causal Graphscited by 48
  5. 2021Unsuitability of NOTEARS for Causal Graph Discoverycited by 47
  6. 2019Scaling structural learning with NO-BEARS to infer causal transcriptome networkscited by 39
  7. 2019The Case for Evaluating Causal Models Using Interventional Measures and Empirical Datacited by 30
  8. 2018High-Dimensional Causal Discovery Under non-Gaussianitycited by 24
  9. 2020On Low Rank Directed Acyclic Graphs and Causal Structure Learningcited by 23
  10. 2020Recent Developments in Boolean Matrix Factorizationcited by 15
  11. 2022From graphs to DAGs: a low-complexity model and a scalable algorithmcited by 5
  12. 2017Structure Learning of Linear Gaussian Structural Equation Models with Weak Edgescited by 4
  13. 2020Binary Matrix Factorisation via Column Generationcited by 3
  14. 2015Identifying Seizure Onset Zone from the Causal Connectivity Inferred Using Directed Informationcited by 2
  15. 2018Ranking Causal Influence of Financial Markets via Directed Information Graphscited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 6; 2023: 7; 2024: 14; 2025: 9; 2026: 11.

47 papers.

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  1. 2023CUTS+: High-dimensional Causal Discovery from Irregular Time-seriescited by 41
  2. 2022Learning Causal Representations of Single Cells via Sparse Mechanism Shift Modelingcited by 34
  3. 2023Stable Differentiable Causal Discoverycited by 31
  4. 2022CausalBench: A Large-scale Benchmark for Network Inference from Single-cell Perturbation Datacited by 29
  5. 2023DynGFN: Towards Bayesian Inference of Gene Regulatory Networks with GFlowNetscited by 27
  6. 2024Sample, estimate, aggregate: A recipe for causal discovery foundation modelscited by 21
  7. 2022Deep Learning of Causal Structures in High Dimensionscited by 20
  8. 2023NODAGS-Flow: Nonlinear Cyclic Causal Structure Learningcited by 20
  9. 2024The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applicationscited by 18
  10. 2024On the Identification of Temporally Causal Representation with Instantaneous Dependencecited by 16
  11. 2022Deep Causal Learning: Representation, Discovery and Inferencecited by 11
  12. 2023Constraint-Free Structure Learning with Smooth Acyclic Orientationscited by 10
35 more
  1. 2024DCILP: A Distributed Approach for Large-Scale Causal Structure Learningcited by 8
  2. 2023The CausalBench challenge: A machine learning contest for gene network inference from single-cell perturbation datacited by 7
  3. 2022Causal inference in drug discovery and developmentcited by 6
  4. 2024Scalable and Flexible Causal Discovery with an Efficient Test for Adjacencycited by 6
  5. 2024Large-Scale Targeted Cause Discovery via Learning from Simulated Datacited by 6
  6. 2024Continuous Bayesian Model Selection for Multivariate Causal Discoverycited by 6
  7. 2025Interpretable Neural ODEs for Gene Regulatory Network Discovery under Perturbationscited by 6
  8. 2024Deriving Causal Order from Single-Variable Interventions: Guarantees & Algorithmcited by 5
  9. 2024AcceleratedLiNGAM: Learning Causal DAGs at the speed of GPUscited by 4
  10. 2024ProDAG: Projected Variational Inference for Directed Acyclic Graphscited by 4
  11. 2024Generative Intervention Models for Causal Perturbation Modelingcited by 4
  12. 2025CausalMan: A physics-based simulator for large-scale causalitycited by 4
  13. 2025Since Faithfulness Fails: The Performance Limits of Neural Causal Discoverycited by 4
  14. 2025Differentiable Cyclic Causal Discovery Under Unmeasured Confounderscited by 4
  15. 2023DiscoGen: Learning to Discover Gene Regulatory Networkscited by 3
  16. 2024Simulation-based Benchmarking for Causal Structure Learning in Gene Perturbation Experimentscited by 3
  17. 2025Characterization and Learning of Causal Graphs from Hard Interventionscited by 2
  18. 2025Causality-informed Anomaly Detection in Partially Observable Sensor Networks: Moving beyond Correlationscited by 2
  19. 2025Robust Causal Discovery under Imperfect Structural Constraintscited by 2
  20. 2022Learning Large Causal Structures from Inverse Covariance Matrix via Sparse Matrix Decompositioncited by 1
  21. 2024Learning to refine domain knowledge for biological network inferencecited by 1
  22. 2024MissNODAG: Differentiable Cyclic Causal Graph Learning from Incomplete Datacited by 1
  23. 2026Unsupervised Causal Abstractions Discoverycited by 1
  24. 2025GPO-VAE: Modeling Explainable Gene Perturbation Responses utilizing GRN-Aligned Parameter Optimizationcited by 0
  25. 2025Large-Scale Bayesian Causal Discovery with Interventional Datacited by 0
  26. 2026Many Experiments, Few Repetitions, Unpaired Data, and Sparse Effects: Is Causal Inference Possible?cited by 0
  27. 2026Partial Causal Structure Learning for Valid Selective Conformal Inference under Interventionscited by 0
  28. 2026Causal Cellular Context Transfer Learning (C3TL): An Efficient Architecture for Prediction of Unseen Perturbation Effectscited by 0
  29. 2026PRCD-MAP: Learning How Much to Trust Imperfect Priors in Causal Discoverycited by 0
  30. 2026When Does Gene Regulatory Network Inference Break? A Controlled Diagnostic Study of Causal and Correlational Methods on Single-Cell Datacited by 0
  31. 2026PACER: Acyclic Causal Discovery from Large-Scale Interventional Datacited by 0
  32. 2026polyDAG: Polynomial Acyclicity Constraints for Efficient Continuous Causal Discovery in Visual Semantic Graphscited by 0
  33. 2026Graphical Causal Reasoning for Root Cause Analysis in Cloud Networkscited by 0
  34. 2026DKCD: Domain Knowledge-Enhanced Causal Discovery from Unstructured Datacited by 0
  35. 2026Amortized Bayesian Causal Discovery of Extended Factor Graphscited by 0