mlsanityData to 7 Oct 2026

Order-based Structure Learning with Normalizing Flows

arXiv 2308.07480 ↗First posted 14 Aug 2023cs.LG stat.MEcited by 4

Not on the map. Why?

Abstract (arXiv)

Estimating the causal structure of observational data is a challenging combinatorial search problem that scales super-exponentially with graph size. Existing methods use continuous relaxations to make this problem computationally tractable but often restrict the data-generating process to additive noise models (ANMs) through explicit or implicit assumptions. We present Order-based Structure Learning with Normalizing Flows (OSLow), a framework that relaxes these assumptions using autoregressive normalizing flows. We leverage the insight that searching over topological orderings is a natural way to enforce acyclicity in structure discovery and propose a novel, differentiable permutation learning method to find such orderings. Through extensive experiments on synthetic and real-world data, we demonstrate that OSLow outperforms prior baselines and improves performance on the observational Sachs and SynTReN datasets as measured by structural hamming distance and structural intervention distance, highlighting the importance of relaxing the ANM assumption made by existing methods.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 38 of its 62 references that are in the map. First posted on arXiv 14 Aug 2023.

Builds on

38 of 62 references.

References · 38

  1. 2015Variational Inference with Normalizing Flowscited by 2,161
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  3. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,539
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  7. 2013Causal Discovery with Continuous Additive Noise Modelscited by 252
  8. 2019Gradient-Based Neural DAG Learningcited by 227
  9. 2021D'ya like DAGs? A Survey on Structure Learning and Causal Discoverycited by 209
  10. 2019Learning Sparse Nonparametric DAGscited by 207
  11. 2019Stochastic Beams and Where to Find Them: The Gumbel-Top-k Trick for Sampling Sequences Without Replacementcited by 205
  12. 2013CAM: Causal additive models, high-dimensional order search and penalized regressioncited by 175
26 more
  1. 2018Learning Latent Permutations with Gumbel-Sinkhorn Networkscited by 172
  2. 2019Causal Discovery with Reinforcement Learningcited by 145
  3. 2022Score matching enables causal discovery of nonlinear additive noise modelscited by 108
  4. 2020Causal Autoregressive Flowscited by 97
  5. 2022Deep End-to-end Causal Inferencecited by 93
  6. 2021BCD Nets: Scalable Variational Approaches for Bayesian Causal Discoverycited by 68
  7. 2013Causal Networks: Semantics and Expressivenesscited by 67
  8. 2022Diffusion Models for Causal Discovery via Topological Orderingcited by 64
  9. 2022Greedy Relaxations of the Sparsest Permutation Algorithmcited by 63
  10. 2018SparseMAP: Differentiable Sparse Structured Inferencecited by 62
  11. 2019Causal Discovery with General Non-Linear Relationships Using Non-Linear ICAcited by 58
  12. 2022On the Identifiability and Estimation of Causal Location-Scale Noise Modelscited by 56
  13. 2018On Causal Discovery with Equal Variance Assumptioncited by 55
  14. 2021Ordering-Based Causal Discovery with Reinforcement Learningcited by 55
  15. 2017Learning linear structural equation models in polynomial time and sample complexitycited by 49
  16. 2022Differentiable DAG Samplingcited by 46
  17. 2022Identifying Patient-Specific Root Causes with the Heteroscedastic Noise Modelcited by 38
  18. 2020A polynomial-time algorithm for learning nonparametric causal graphscited by 29
  19. 2017Bayesian Network Learning via Topological Ordercited by 14
  20. 2021Efficient Bayesian network structure learning via local Markov boundary searchcited by 14
  21. 2023DAG Learning on the Permutahedroncited by 9
  22. 2013On Sampling from the Gibbs Distribution with Random Maximum A-Posteriori Perturbationscited by 7
  23. 2013An Algorithm for the Construction of Bayesian Network Structures from Datacited by 5
  24. 2013Optimizing Causal Orderings for Generating DAGs from Datacited by 5
  25. 2022Sequentially learning the topological ordering of causal directed acyclic graphs with likelihood ratio scorescited by 3
  26. 2019Conditionally-additive-noise Models for Structure Learningcited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 2; 2026: 1.

4 papers.

  1. 2025CausalPFN: Amortized Causal Effect Estimation via In-Context Learningcited by 43
  2. 2024A Geometric View of Data Complexity: Efficient Local Intrinsic Dimension Estimation with Diffusion Modelscited by 41
  3. 2025Skewness-Robust Causal Discovery in Location-Scale Noise Modelscited by 1
  4. 2026Learning the Structure of Triangular Transport Mapscited by 0