mlsanityData to 7 Oct 2026

Variational Causal Networks: Approximate Bayesian Inference over Causal Structures

arXiv 2106.07635 ↗First posted 14 Jun 2021cs.LG cs.AI stat.MLcited by 43

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Abstract (arXiv)

Learning the causal structure that underlies data is a crucial step towards robust real-world decision making. The majority of existing work in causal inference focuses on determining a single directed acyclic graph (DAG) or a Markov equivalence class thereof. However, a crucial aspect to acting intelligently upon the knowledge about causal structure which has been inferred from finite data demands reasoning about its uncertainty. For instance, planning interventions to find out more about the causal mechanisms that govern our data requires quantifying epistemic uncertainty over DAGs. While Bayesian causal inference allows to do so, the posterior over DAGs becomes intractable even for a small number of variables. Aiming to overcome this issue, we propose a form of variational inference over the graphs of Structural Causal Models (SCMs). To this end, we introduce a parametric variational family modelled by an autoregressive distribution over the space of discrete DAGs. Its number of parameters does not grow exponentially with the number of variables and can be tractably learned by maximising an Evidence Lower Bound (ELBO). In our experiments, we demonstrate that the proposed variational posterior is able to provide a good approximation of the true posterior.

Key facts. Cited by 43 papers in the map (data through 7 Oct 2026). Builds on 20 of its 37 references that are in the map. First posted on arXiv 14 Jun 2021.

Builds on

20 of 37 references.

References · 20

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2016Variational Inference: A Review for Statisticianscited by 1,466
  3. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 745
  4. 2015Causal inference using invariant prediction: identification and confidence intervalscited by 533
  5. 2019DAG-GNN: DAG Structure Learning with Graph Neural Networkscited by 329
  6. 2019Gradient-Based Neural DAG Learningcited by 227
  7. 2013CAM: Causal additive models, high-dimensional order search and penalized regressioncited by 175
  8. 2019A Meta-Transfer Objective for Learning to Disentangle Causal Mechanismscited by 158
  9. 2017Invariant Causal Prediction for Nonlinear Modelscited by 140
  10. 2019Learning Neural Causal Models from Unknown Interventionscited by 113
  11. 2017Backpropagation through the Void: Optimizing control variates for black-box gradient estimationcited by 104
  12. 2017Causal Structure Learningcited by 84
8 more
  1. 2019Integer Discrete Flows and Lossless Compressioncited by 82
  2. 2019Discrete Flows: Invertible Generative Models of Discrete Datacited by 68
  3. 2019ABCD-Strategy: Budgeted Experimental Design for Targeted Causal Structure Discoverycited by 52
  4. 2013Parameter Priors for Directed Acyclic Graphical Models and the Characterization of Several Probability Distributionscited by 41
  5. 2015Partition MCMC for inference on acyclic digraphscited by 33
  6. 2014Addendum on the scoring of Gaussian directed acyclic graphical modelscited by 32
  7. 2020Amortized learning of neural causal representationscited by 14
  8. 2018Minimal I-MAP MCMC for Scalable Structure Discovery in Causal DAG Modelscited by 11

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 14; 2023: 11; 2024: 8; 2025: 3; 2026: 5.

43 papers.

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  1. 2022TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Secondcited by 643
  2. 2022Bayesian Structure Learning with Generative Flow Networkscited by 153
  3. 2022Deep End-to-end Causal Inferencecited by 93
  4. 2023GFlowNets for AI-Driven Scientific Discoverycited by 63
  5. 2023Joint Bayesian Inference of Graphical Structure and Parameters with a Single Generative Flow Networkcited by 50
  6. 2022Interventions, Where and How? Experimental Design for Causal Models at Scalecited by 49
  7. 2021Learning Neural Causal Models with Active Interventionscited by 40
  8. 2022Active Bayesian Causal Inferencecited by 34
  9. 2023BayesDAG: Gradient-Based Posterior Inference for Causal Discoverycited by 33
  10. 2022Bayesian learning of Causal Structure and Mechanisms with GFlowNets and Variational Bayescited by 30
  11. 2023DynGFN: Towards Bayesian Inference of Gene Regulatory Networks with GFlowNetscited by 27
  12. 2022BaCaDI: Bayesian Causal Discovery with Unknown Interventionscited by 26
31 more
  1. 2024A Meta-Learning Approach to Bayesian Causal Discoverycited by 22
  2. 2021GeneDisco: A Benchmark for Experimental Design in Drug Discoverycited by 18
  3. 2024Identifiable Exchangeable Mechanisms for Causal Structure and Representation Learningcited by 16
  4. 2022Tractable Uncertainty for Structure Learningcited by 15
  5. 2023Differentiable Multi-Target Causal Bayesian Experimental Designcited by 15
  6. 2022On the Generalization and Adaption Performance of Causal Modelscited by 8
  7. 2023A Survey of Methods, Challenges and Perspectives in Causalitycited by 6
  8. 2024Effective Bayesian Causal Inference via Structural Marginalisation and Autoregressive Orderscited by 6
  9. 2022Learning Latent Structural Causal Modelscited by 5
  10. 2022Trust Your nabla: Gradient-based Intervention Targeting for Causal Discoverycited by 5
  11. 2023Causal Inference in Gene Regulatory Networks with GFlowNet: Towards Scalability in Large Systemscited by 5
  12. 2024Challenges and Considerations in the Evaluation of Bayesian Causal Discoverycited by 5
  13. 2023CO-BED: Information-Theoretic Contextual Optimization via Bayesian Experimental Designcited by 4
  14. 2024Permutation-based Inference for Variational Learning of Directed Acyclic Graphscited by 4
  15. 2024ProDAG: Projected Variational Inference for Directed Acyclic Graphscited by 4
  16. 2022Efficient Real-world Testing of Causal Decision Making via Bayesian Experimental Design for Contextual Optimisationcited by 3
  17. 2022Learning Multiscale Non-stationary Causal Structurescited by 3
  18. 2023Causal structure learning with momentum: Sampling distributions over Markov Equivalence Classes of DAGscited by 2
  19. 2022Latent Variable Models for Bayesian Causal Discoverycited by 1
  20. 2023Causal Graph Discovery from Self and Mutually Exciting Time Seriescited by 1
  21. 2023Disentanglement of Latent Representations via Causal Interventionscited by 1
  22. 2025Goal-Oriented Sequential Bayesian Experimental Design for Causal Learningcited by 1
  23. 2024Disentangled Representations for Causal Cognitioncited by 0
  24. 2024Enhancing Solution Efficiency in Reinforcement Learning: Leveraging Sub-GFlowNet and Entropy Integrationcited by 0
  25. 2025Causal Bayesian Optimization with Unknown Graphscited by 0
  26. 2025Graph Distance Based on Cause-Effect Estimands with Latentscited by 0
  27. 2026Iterative Causal Discovery: Per-Edge Impossibility Certificates, Tier-Aware Oracle Queries, and the 1+K Lower Boundcited by 0
  28. 2026Causal Atlases from Entropic Inference: Bayesian Networks beyond Optimal DAGscited by 0
  29. 2026SVI-DAG: A Structured Variational Inference Approach to Bayesian Causal Discoverycited by 0
  30. 2026Interpretable Causal Discovery via Causal-Effect Constraintscited by 0
  31. 2026Joint Causal Structure and Cluster Discovery Using Variational Inferencecited by 0