mlsanityData to 7 Oct 2026

Permutation-based Inference for Variational Learning of Directed Acyclic Graphs

arXiv 2402.02644 ↗First posted 4 Feb 2024cs.LG stat.MLcited by 4

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Abstract (arXiv)

Estimating the structure of Bayesian networks as directed acyclic graphs (DAGs) from observational data is a fundamental challenge, particularly in causal discovery. Bayesian approaches excel by quantifying uncertainty and addressing identifiability, but key obstacles remain: (i) representing distributions over DAGs and (ii) estimating a posterior in the underlying combinatorial space. We introduce PIVID, a method that jointly infers a distribution over permutations and DAGs using variational inference and continuous relaxations of discrete distributions. Through experiments on synthetic and real-world datasets, we show that PIVID can outperform deterministic and Bayesian approaches, achieving superior accuracy-uncertainty trade-offs while scaling efficiently with the number of variables.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 23 of its 49 references that are in the map. First posted on arXiv 4 Feb 2024.

Builds on

23 of 49 references.

References · 23

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  2. 2016Optimization Methods for Large-Scale Machine Learningcited by 1,140
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11 more
  1. 2021Efficient Neural Causal Discovery without Acyclicity Constraintscited by 82
  2. 2021BCD Nets: Scalable Variational Approaches for Bayesian Causal Discoverycited by 68
  3. 2020SoftSort: A Continuous Relaxation for the argsort Operatorcited by 66
  4. 2021gCastle: A Python Toolbox for Causal Discoverycited by 60
  5. 2023Joint Bayesian Inference of Graphical Structure and Parameters with a Single Generative Flow Networkcited by 50
  6. 2022Differentiable DAG Samplingcited by 46
  7. 2021Variational Causal Networks: Approximate Bayesian Inference over Causal Structurescited by 43
  8. 2020Graphical Normalizing Flowscited by 37
  9. 2023BayesDAG: Gradient-Based Posterior Inference for Causal Discoverycited by 33
  10. 2022Tractable Uncertainty for Structure Learningcited by 15
  11. 2021Learning Bayesian Networks through Birkhoff Polytope: A Relaxation Methodcited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 0; 2026: 2.

4 papers.

  1. 2024Optimal Transport for Structure Learning Under Missing Datacited by 5
  2. 2024ProDAG: Projected Variational Inference for Directed Acyclic Graphscited by 4
  3. 2026Arrow: A Foundation Model for Causal Discoverycited by 4
  4. 2026Causal Preference Elicitationcited by 0