Ordering-based Causal Discovery via Generalized Score Matching
Not on the map. Why?
Abstract (arXiv)
Learning DAG structures from purely observational data remains a long-standing challenge across scientific domains. An emerging line of research leverages the score of the data distribution to initially identify a topological order of the underlying DAG via leaf node detection and subsequently performs edge pruning for graph recovery. This paper extends the score matching framework for causal discovery, which is originally designated for continuous data, and introduces a novel leaf discriminant criterion based on the discrete score function. Through simulated and real-world experiments, we demonstrate that our theory enables accurate inference of true causal orders from observed discrete data and the identified ordering can significantly boost the accuracy of existing causal discovery baselines on nearly all of the settings.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 36 of its 92 references that are in the map. First posted on arXiv 22 Jan 2026.
Builds on
36 of 92 references.
References · 36
- 2014Adam: A Method for Stochastic Optimizationcited by 36,960
- 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
- 2023Discrete Diffusion Modeling by Estimating the Ratios of the Data Distributioncited by 712
- 2022A Continuous Time Framework for Discrete Denoising Modelscited by 437
- 2019Sliced Score Matching: A Scalable Approach to Density and Score Estimationcited by 381
- 2019DAG-GNN: DAG Structure Learning with Graph Neural Networkscited by 329
- 2013Causal Discovery with Continuous Additive Noise Modelscited by 252
- 2019Gradient-Based Neural DAG Learningcited by 227
- 2021D'ya like DAGs? A Survey on Structure Learning and Causal Discoverycited by 209
- 2019Learning Sparse Nonparametric DAGscited by 207
- 2013Learning Bayesian Networks: The Combination of Knowledge and Statistical Datacited by 185
- 2013CAM: Causal additive models, high-dimensional order search and penalized regressioncited by 175
24 more
- 2022Score-based Continuous-time Discrete Diffusion Modelscited by 167
- 2022Concrete Score Matching: Generalized Score Matching for Discrete Datacited by 144
- 2022DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterizationcited by 135
- 2022Score matching enables causal discovery of nonlinear additive noise modelscited by 108
- 2021A survey of Bayesian Network structure learningcited by 85
- 2022Diffusion Models for Causal Discovery via Topological Orderingcited by 64
- 2017Gradient Estimators for Implicit Modelscited by 58
- 2018On Causal Discovery with Equal Variance Assumptioncited by 55
- 2017Learning linear structural equation models in polynomial time and sample complexitycited by 49
- 2022Denoising Likelihood Score Matching for Conditional Score-based Data Generationcited by 45
- 2023Scalable Causal Discovery with Score Matchingcited by 42
- 2023Causal Discovery with Score Matching on Additive Models with Arbitrary Noisecited by 41
- 2023Assumption violations in causal discovery and the robustness of score matchingcited by 28
- 2016Entropic Causal Inferencecited by 27
- 2023Sample Complexity Bounds for Score-Matching: Causal Discovery and Generative Modelingcited by 15
- 2021Entropic Causal Inference: Identifiability and Finite Sample Resultscited by 12
- 2024Ordering-Based Causal Discovery for Linear and Nonlinear Relationscited by 11
- 2018Causal Inference on Discrete Data via Estimating Distance Correlationscited by 8
- 2024Score matching through the roof: linear, nonlinear, and latent variables causal discoverycited by 8
- 2022Ordinal Causal Discoverycited by 5
- 2024Optimal Transport for Structure Learning Under Missing Datacited by 5
- 2023Shortcuts for causal discovery of nonlinear models by score matchingcited by 4
- 2020Learning Bayesian Networks from Ordinal Datacited by 3
- 2025Entropic Causal Inference: Graph Identifiabilitycited by 3
Built on by
Citing papers per year: 2026: 1.
1 paper.