mlsanityData to 14 Oct 2026

Ordering-Based Causal Discovery for Linear and Nonlinear Relations

arXiv 2410.05890 ↗First posted 8 Oct 2024cs.LGcited by 13

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Abstract (arXiv)

Identifying causal relations from purely observational data typically requires additional assumptions on relations and/or noise. Most current methods restrict their analysis to datasets that are assumed to have pure linear or nonlinear relations, which is often not reflective of real-world datasets that contain a combination of both. This paper presents CaPS, an ordering-based causal discovery algorithm that effectively handles linear and nonlinear relations. CaPS introduces a novel identification criterion for topological ordering and incorporates the concept of "parent score" during the post-processing optimization stage. These scores quantify the strength of the average causal effect, helping to accelerate the pruning process and correct inaccurate predictions in the pruning step. Experimental results demonstrate that our proposed solutions outperform state-of-the-art baselines on synthetic data with varying ratios of linear and nonlinear relations. The results obtained from real-world data also support the competitiveness of CaPS. Code and datasets are available at https://github.com/E2real/CaPS.

Key facts. Cited by 13 papers in the map (data through 14 Oct 2026). Builds on 21 of its 35 references that are in the map. First posted on arXiv 8 Oct 2024.

Builds on

21 of 35 references.

References · 21

  1. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 752
  2. 2019DAG-GNN: DAG Structure Learning with Graph Neural Networkscited by 331
  3. 2013Causal Discovery with Continuous Additive Noise Modelscited by 255
  4. 2019Gradient-Based Neural DAG Learningcited by 227
  5. 2019Learning Sparse Nonparametric DAGscited by 207
  6. 2020On the Role of Sparsity and DAG Constraints for Learning Linear DAGscited by 191
  7. 2013CAM: Causal additive models, high-dimensional order search and penalized regressioncited by 178
  8. 2021Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Gamecited by 161
  9. 2022DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterizationcited by 140
  10. 2019Learning Neural Causal Models from Unknown Interventionscited by 113
  11. 2022Score matching enables causal discovery of nonlinear additive noise modelscited by 111
  12. 2013High-dimensional learning of linear causal networks via inverse covariance estimationcited by 87
9 more
  1. 2022Diffusion Models for Causal Discovery via Topological Orderingcited by 66
  2. 2017Gradient Estimators for Implicit Modelscited by 58
  3. 2019A Graph Autoencoder Approach to Causal Structure Learningcited by 55
  4. 2017Learning linear structural equation models in polynomial time and sample complexitycited by 51
  5. 2022Differentiable DAG Samplingcited by 47
  6. 2020CASTLE: Regularization via Auxiliary Causal Graph Discoverycited by 41
  7. 2023Optimizing NOTEARS Objectives via Topological Swapscited by 17
  8. 2020Amortized learning of neural causal representationscited by 14
  9. 2023DAG Learning on the Permutahedroncited by 9

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 5; 2026: 7.

13 papers.

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  1. 2025Non-stationary Diffusion For Probabilistic Time Series Forecastingcited by 27
  2. 2025Causal Discovery via Quantile Partial Effectcited by 4
  3. 2025Score-informed Neural Operator for Enhancing Ordering-based Causal Discoverycited by 2
  4. 2025Causal Ordering for Structure Learning from Time Seriescited by 2
  5. 2026DAG-FM: A Foundation Model for Causal Discovery under Heterogeneous Causal Mechanismscited by 2
  6. 2024LoSAM: Local Search in Additive Noise Models with Mixed Mechanisms and General Noise for Global Causal Discoverycited by 1
  7. 2025When Additive Noise Meets Unobserved Mediators: Bivariate Denoising Diffusion for Causal Discoverycited by 1
  8. 2026Ordering-based Causal Discovery via Generalized Score Matchingcited by 1
  9. 2026Order-based Rehearsal Learningcited by 1
  10. 2026Sparse Additive Model Pruning for Order-Based Causal Structure Learningcited by 0
  11. 2026TriOpt: A Scalable Algorithm for Linear Causal Discoverycited by 0
  12. 2026Hold-Out Scoring for Efficient Gaussian DAG Learningcited by 0
1 more
  1. 2026Local Fisher Information Enables Sparse Causal Discoverycited by 0