mlsanityData to 7 Oct 2026

Partition MCMC for inference on acyclic digraphs

arXiv 1504.05006 ↗First posted 20 Apr 2015stat.ML stat.CO stat.MEcited by 33

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Abstract (arXiv)

Acyclic digraphs are the underlying representation of Bayesian networks, a widely used class of probabilistic graphical models. Learning the underlying graph from data is a way of gaining insights about the structural properties of a domain. Structure learning forms one of the inference challenges of statistical graphical models. MCMC methods, notably structure MCMC, to sample graphs from the posterior distribution given the data are probably the only viable option for Bayesian model averaging. Score modularity and restrictions on the number of parents of each node allow the graphs to be grouped into larger collections, which can be scored as a whole to improve the chain's convergence. Current examples of algorithms taking advantage of grouping are the biased order MCMC, which acts on the alternative space of permuted triangular matrices, and non ergodic edge reversal moves. Here we propose a novel algorithm, which employs the underlying combinatorial structure of DAGs to define a new grouping. As a result convergence is improved compared to structure MCMC, while still retaining the property of producing an unbiased sample. Finally the method can be combined with edge reversal moves to improve the sampler further.

Key facts. Cited by 33 papers in the map (data through 7 Oct 2026). First posted on arXiv 20 Apr 2015.

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Citing papers per year: 2021: 5; 2022: 7; 2023: 5; 2024: 8; 2025: 5; 2026: 3.

33 papers.

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  1. 2022Bayesian Structure Learning with Generative Flow Networkscited by 153
  2. 2021DiBS: Differentiable Bayesian Structure Learningcited by 105
  3. 2021A survey of Bayesian Network structure learningcited by 85
  4. 2022Differentiable DAG Samplingcited by 46
  5. 2022Causal Structure Learning: a Combinatorial Perspectivecited by 46
  6. 2021Variational Causal Networks: Approximate Bayesian Inference over Causal Structurescited by 43
  7. 2023BayesDAG: Gradient-Based Posterior Inference for Causal Discoverycited by 33
  8. 2021Bayesian structure learning and sampling of Bayesian networks with the R package BiDAGcited by 17
  9. 2022Tractable Uncertainty for Structure Learningcited by 15
  10. 2022Causal Entropy Optimizationcited by 13
  11. 2023Computably Continuous Reinforcement-Learning Objectives are PAC-learnablecited by 13
  12. 2021Benchpress: A Scalable and Versatile Workflow for Benchmarking Structure Learning Algorithmscited by 11
21 more
  1. 2025Estimating Interventional Distributions with Uncertain Causal Graphs through Meta-Learningcited by 11
  2. 2024Effective Bayesian Causal Inference via Structural Marginalisation and Autoregressive Orderscited by 6
  3. 2022The interventional Bayesian Gaussian equivalent score for Bayesian causal inference with unknown soft interventionscited by 4
  4. 2023A Bayesian Take on Gaussian Process Networkscited by 4
  5. 2023Structure Learning with Adaptive Random Neighborhood Informed MCMCcited by 4
  6. 2024Possible Principles for Aligned Structure Learning Agentscited by 3
  7. 2023Causal structure learning with momentum: Sampling distributions over Markov Equivalence Classes of DAGscited by 2
  8. 2024Bayesian Causal Inference with Gaussian Process Networkscited by 2
  9. 2024Greedy equivalence search for nonparametric graphical modelscited by 2
  10. 2026Test-Time Learning of Causal Structure from Interventional Datacited by 2
  11. 2025Covariate Dependent Mixture of Bayesian Networkscited by 1
  12. 2025Lower Bounds on the Size of Markov Equivalence Classescited by 1
  13. 2025Consistent Bayesian causal discovery for structural equation models with equal error variancescited by 1
  14. 2022Reinforcement Causal Structure Learning on Order Graphcited by 0
  15. 2024Scalable Structure Learning for Sparse Context-Specific Systemscited by 0
  16. 2024Exact discovery is polynomial for certain sparse causal Bayesian networkscited by 0
  17. 2024Enhancing Solution Efficiency in Reinforcement Learning: Leveraging Sub-GFlowNet and Entropy Integrationcited by 0
  18. 2024Optimal Particle-based Approximation of Discrete Distributions (OPAD)cited by 0
  19. 2025Scaling Up Bayesian DAG Samplingcited by 0
  20. 2026Interpretable Causal Discovery via Causal-Effect Constraintscited by 0
  21. 2026MARCEDES: Score-based causal discovery under non-Gaussianity with continuous optimizationcited by 0