mlsanityData to 7 Oct 2026

Parameter Priors for Directed Acyclic Graphical Models and the Characterization of Several Probability Distributions

arXiv 1301.6697 ↗First posted 23 Jan 2013cs.LG stat.MLcited by 41

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Abstract (arXiv)

We show that the only parameter prior for complete Gaussian DAG models that satisfies global parameter independence, complete model equivalence, and some weak regularity assumptions, is the normal-Wishart distribution. Our analysis is based on the following new characterization of the Wishart distribution: let W be an n x n, n >= 3, positive-definite symmetric matrix of random variables and f(W) be a pdf of W. Then, f(W) is a Wishart distribution if and only if W_{11}-W_{12}W_{22}^{-1}W_{12}' is independent of {W_{12}, W_{22}} for every block partitioning W_{11}, W_{12}, W_{12}', W_{22} of W. Similar characterizations of the normal and normal-Wishart distributions are provided as well. We also show how to construct a prior for every DAG model over X from the prior of a single regression model.

Key facts. Cited by 41 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 Jan 2013.

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Citing papers per year: 2021: 6; 2022: 5; 2023: 9; 2024: 10; 2025: 5; 2026: 6.

41 papers.

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  1. 2021DiBS: Differentiable Bayesian Structure Learningcited by 105
  2. 2021A survey of Bayesian Network structure learningcited by 85
  3. 2022Causal Structure Learning: a Combinatorial Perspectivecited by 46
  4. 2021Variational Causal Networks: Approximate Bayesian Inference over Causal Structurescited by 43
  5. 2023BayesDAG: Gradient-Based Posterior Inference for Causal Discoverycited by 33
  6. 2022Active Learning for Optimal Intervention Design in Causal Modelscited by 30
  7. 2022BaCaDI: Bayesian Causal Discovery with Unknown Interventionscited by 26
  8. 2024A Meta-Learning Approach to Bayesian Causal Discoverycited by 22
  9. 2021Bayesian structure learning and sampling of Bayesian networks with the R package BiDAGcited by 17
  10. 2023Optimizing NOTEARS Objectives via Topological Swapscited by 17
  11. 2024Causal Discovery with Fewer Conditional Independence Testscited by 13
  12. 2021Benchpress: A Scalable and Versatile Workflow for Benchmarking Structure Learning Algorithmscited by 11
29 more
  1. 2023Bivariate Causal Discovery using Bayesian Model Selectioncited by 11
  2. 2025Estimating Interventional Distributions with Uncertain Causal Graphs through Meta-Learningcited by 11
  3. 2021Structure learning in polynomial time: Greedy algorithms, Bregman information, and exponential familiescited by 10
  4. 2023Causality-Aided Trade-off Analysis for Machine Learning Fairnesscited by 6
  5. 2024Better Simulations for Validating Causal Discovery with the DAG-Adaptation of the Onion Methodcited by 6
  6. 2024Challenges and Considerations in the Evaluation of Bayesian Causal Discoverycited by 5
  7. 2024Continuous Bayesian Model Selection for Multivariate Causal Discoverycited by 5
  8. 2022The interventional Bayesian Gaussian equivalent score for Bayesian causal inference with unknown soft interventionscited by 4
  9. 2023A Bayesian Take on Gaussian Process Networkscited by 4
  10. 2023Structure Learning with Adaptive Random Neighborhood Informed MCMCcited by 4
  11. 2023Bayesian causal discovery from unknown general interventionscited by 2
  12. 2024Bayesian Causal Inference with Gaussian Process Networkscited by 2
  13. 2022BCDAG: An R package for Bayesian structure and Causal learning of Gaussian DAGscited by 1
  14. 2025Covariate Dependent Mixture of Bayesian Networkscited by 1
  15. 2025Consistent Bayesian causal discovery for structural equation models with equal error variancescited by 1
  16. 2026On the Number of Conditional Independence Tests in Constraint-based Causal Discoverycited by 1
  17. 2023Bayesian Causal Inference in Doubly Gaussian DAG-probit Modelscited by 0
  18. 2023Scalable Bayesian Structure Learning for Gaussian Graphical Models Using Marginal Pseudo-likelihoodcited by 0
  19. 2024Membership Testing in Markov Equivalence Classes via Independence Query Oraclescited by 0
  20. 2024Exact discovery is polynomial for certain sparse causal Bayesian networkscited by 0
  21. 2024Learning Dynamic Bayesian Networks from Data: Foundations, First Principles and Numerical Comparisonscited by 0
  22. 2024Optimal Particle-based Approximation of Discrete Distributions (OPAD)cited by 0
  23. 2025Large-Scale Bayesian Causal Discovery with Interventional Datacited by 0
  24. 2025Scaling Up Bayesian DAG Samplingcited by 0
  25. 2026PRIM: Meta-Learned Bayesian Root Cause Analysiscited by 0
  26. 2026How Does Bayesian Causal Discovery Fail? Characterising Structural Consequences in Linear Gaussian Networks under Latent Confoundingcited by 0
  27. 2026Interpretable Causal Discovery via Causal-Effect Constraintscited by 0
  28. 2026Joint Causal Structure and Cluster Discovery Using Variational Inferencecited by 0
  29. 2026MARCEDES: Score-based causal discovery under non-Gaussianity with continuous optimizationcited by 0