mlsanityData to 7 Oct 2026

Differentiable DAG Sampling

arXiv 2203.08509 ↗First posted 16 Mar 2022cs.LG stat.MLcited by 46

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Abstract (arXiv)

We propose a new differentiable probabilistic model over DAGs (DP-DAG). DP-DAG allows fast and differentiable DAG sampling suited to continuous optimization. To this end, DP-DAG samples a DAG by successively (1) sampling a linear ordering of the node and (2) sampling edges consistent with the sampled linear ordering. We further propose VI-DP-DAG, a new method for DAG learning from observational data which combines DP-DAG with variational inference. Hence,VI-DP-DAG approximates the posterior probability over DAG edges given the observed data. VI-DP-DAG is guaranteed to output a valid DAG at any time during training and does not require any complex augmented Lagrangian optimization scheme in contrast to existing differentiable DAG learning approaches. In our extensive experiments, we compare VI-DP-DAG to other differentiable DAG learning baselines on synthetic and real datasets. VI-DP-DAG significantly improves DAG structure and causal mechanism learning while training faster than competitors.

Key facts. Cited by 46 papers in the map (data through 7 Oct 2026). Builds on 24 of its 50 references that are in the map. First posted on arXiv 16 Mar 2022.

Builds on

24 of 50 references.

References · 24

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2013Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computationcited by 2,031
  3. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 745
  4. 2019DAG-GNN: DAG Structure Learning with Graph Neural Networkscited by 329
  5. 2013Causal Discovery with Continuous Additive Noise Modelscited by 252
  6. 2019Gradient-Based Neural DAG Learningcited by 227
  7. 2020Differentiable Causal Discovery from Interventional Datacited by 218
  8. 2021D'ya like DAGs? A Survey on Structure Learning and Causal Discoverycited by 209
  9. 2019Stochastic Beams and Where to Find Them: The Gumbel-Top-k Trick for Sampling Sequences Without Replacementcited by 205
  10. 2013CAM: Causal additive models, high-dimensional order search and penalized regressioncited by 175
  11. 2018Learning Latent Permutations with Gumbel-Sinkhorn Networkscited by 172
  12. 2020Erdos Goes Neural: an Unsupervised Learning Framework for Combinatorial Optimization on Graphscited by 115
12 more
  1. 2021Oops I Took A Gradient: Scalable Sampling for Discrete Distributionscited by 92
  2. 2019Masked Gradient-Based Causal Structure Learningcited by 89
  3. 2020Gradient Estimation with Stochastic Softmax Trickscited by 66
  4. 2020SoftSort: A Continuous Relaxation for the argsort Operatorcited by 66
  5. 2021DAGs with No Curl: An Efficient DAG Structure Learning Approachcited by 53
  6. 2020Graphical Normalizing Flowscited by 37
  7. 2015Partition MCMC for inference on acyclic digraphscited by 33
  8. 2020Towards Scalable Bayesian Learning of Causal DAGscited by 33
  9. 2018Efficient Sampling and Structure Learning of Bayesian Networkscited by 28
  10. 2017Bayesian Network Learning via Topological Ordercited by 14
  11. 2014Advances in Learning Bayesian Networks of Bounded Treewidthcited by 10
  12. 2021Probabilistic DAG Searchcited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 5; 2023: 13; 2024: 12; 2025: 7; 2026: 9.

46 papers.

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  1. 2022Weakly supervised causal representation learningcited by 140
  2. 2023Joint Bayesian Inference of Graphical Structure and Parameters with a Single Generative Flow Networkcited by 50
  3. 2023Structure Learning with Continuous Optimization: A Sober Look and Beyondcited by 34
  4. 2023BayesDAG: Gradient-Based Posterior Inference for Causal Discoverycited by 33
  5. 2024A Meta-Learning Approach to Bayesian Causal Discoverycited by 22
  6. 2024Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processescited by 18
  7. 2023CoLiDE: Concomitant Linear DAG Estimationcited by 12
  8. 2024Ordering-Based Causal Discovery for Linear and Nonlinear Relationscited by 11
  9. 2025Estimating Interventional Distributions with Uncertain Causal Graphs through Meta-Learningcited by 11
  10. 2023Constraint-Free Structure Learning with Smooth Acyclic Orientationscited by 10
  11. 2023DAG Learning on the Permutahedroncited by 9
  12. 2023Learning DAGs from Data with Few Root Causescited by 8
34 more
  1. 2024Effective Bayesian Causal Inference via Structural Marginalisation and Autoregressive Orderscited by 6
  2. 2022Learning Latent Structural Causal Modelscited by 5
  3. 2023Order-based Structure Learning with Normalizing Flowscited by 4
  4. 2024Permutation-based Inference for Variational Learning of Directed Acyclic Graphscited by 4
  5. 2024ProDAG: Projected Variational Inference for Directed Acyclic Graphscited by 4
  6. 2024Sample Efficient Bayesian Learning of Causal Graphs from Interventionscited by 4
  7. 2026Arrow: A Foundation Model for Causal Discoverycited by 4
  8. 2022Learning Multiscale Non-stationary Causal Structurescited by 3
  9. 2022Learning Discrete Directed Acyclic Graphs via Backpropagationcited by 3
  10. 2023CMVAE: Causal Meta VAE for Unsupervised Meta-Learningcited by 3
  11. 2023Tree Search in DAG Space with Model-based Reinforcement Learning for Causal Discoverycited by 3
  12. 2024Reinforcement Learning for Causal Discovery without Acyclicity Constraintscited by 3
  13. 2025Learning Identifiable Structures Helps Avoid Bias in DNN-based Supervised Causal Learningcited by 3
  14. 2023Context-Aware Bayesian Network Actor-Critic Methods for Cooperative Multi-Agent Reinforcement Learningcited by 2
  15. 2026A Knowledge-Informed Pretrained Model for Causal Discoverycited by 2
  16. 2026Concomitant DAG Learning: On the Roles of Noise Adaptivity, Sparsity, and Non-negativitycited by 2
  17. 2022Latent Variable Models for Bayesian Causal Discoverycited by 1
  18. 2023Towards Human-like Perception: Learning Structural Causal Model in Heterogeneous Graphcited by 1
  19. 2024Scalable Variational Causal Discovery Unconstrained by Acyclicitycited by 1
  20. 2024Causal Order Discovery based on Monotonic SCMscited by 1
  21. 2025Your Assumed DAG is Wrong and Here's How To Deal With Itcited by 1
  22. 2025Incorporating Expert Knowledge into Bayesian Causal Discovery of Mixtures of Directed Acyclic Graphscited by 1
  23. 2025MetaCaDI: A Meta-Learning Framework for Causal Discovery from Multiple Environments with Unknown Interventionscited by 1
  24. 2025Amortized Causal Discovery with Prior-Fitted Networkscited by 1
  25. 2023Joint Distributional Learning via Cramer-Wold Distancecited by 0
  26. 2024Implicit Causal Representation Learning via Switchable Mechanismscited by 0
  27. 2024Causal Learning in Biomedical Applications: Krebs Cycle as a Benchmarkcited by 0
  28. 2025Towards Unsupervised Causal Representation Learning via Latent Additive Noise Model Causal Autoencoderscited by 0
  29. 2026DAGAF: A directed acyclic generative adversarial framework for joint structure learning and tabular data synthesiscited by 0
  30. 2026Learning Temporal Causal Structure via Smooth Differentiable Optimizationcited by 0
  31. 2026polyDAG: Polynomial Acyclicity Constraints for Efficient Continuous Causal Discovery in Visual Semantic Graphscited by 0
  32. 2026Amortized Bayesian Causal Discovery of Extended Factor Graphscited by 0
  33. 2026SVI-DAG: A Structured Variational Inference Approach to Bayesian Causal Discoverycited by 0
  34. 2026Learning the Structure of Triangular Transport Mapscited by 0