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DAG-CLIP: A DAG Learning Framework in the Presence of Latent Variables

arXiv 2610.06086 ↗First posted 5 Oct 2026stat.ME stat.MLcited by 0

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Abstract (arXiv)

Learning directed acyclic graphs (DAGs) to uncover causal mechanisms has attracted substantial attention in machine learning. While most existing methods focus exclusively on observed variables, many variables of substantive interest are latent constructs defined by statistical measurement models. Such constructs are particularly common in the social and behavioral sciences. In this paper, we propose a general statistical framework for DAG learning when some or all nodes of the graph are latent variables, accommodating non-Gaussian manifest variables such as binary and categorical data in the measurement model. To overcome the computational burden of high-dimensional integration in standard marginal likelihoods, we develop DAG learning via Composite-Likelihood-based screening and Iterative Pruning (DAG-CLIP), a two-step composite-likelihood-based learning algorithm. This algorithm first solves a smooth acyclicity-constrained optimization problem to screen out misspecified DAG structures, and subsequently performs BIC-guided composite-likelihood backward deletion within the Markov equivalence class (MEC) space to identify a sparse DAG. We establish the statistical consistency of the algorithm in recovering the MEC of the true DAG, and demonstrate its effectiveness through extensive simulation studies and a real-world application to large-scale educational survey data.

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References · 30

  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. 2020On the Role of Sparsity and DAG Constraints for Learning Linear DAGscited by 191
  4. 2013Causal Inference and Causal Explanation with Background Knowledgecited by 170
  5. 2022DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterizationcited by 140
  6. 2013Learning Equivalence Classes of Bayesian Networks Structurescited by 77
  7. 2018On Causal Discovery with Equal Variance Assumptioncited by 59
  8. 2022Latent Hierarchical Causal Structure Discovery with Rank Constraintscited by 51
  9. 2015High-dimensional consistency in score-based and hybrid structure learningcited by 46
  10. 2014Concave Penalized Estimation of Sparse Gaussian Bayesian Networkscited by 28
  11. 2020Vintage Factor Analysis with Varimax Performs Statistical Inferencecited by 17
  12. 2021Item Response Theory -- A Statistical Framework for Educational and Psychological Measurementcited by 17
18 more
  1. 2021Integer Programming for Causal Structure Learning in the Presence of Latent Variablescited by 15
  2. 2023Discovery and inference of a causal network with hidden confoundingcited by 8
  3. 2020Improving Bayesian Network Structure Learning in the Presence of Measurement Errorcited by 6
  4. 2021Learning linear non-Gaussian directed acyclic graph with diverging number of nodescited by 6
  5. 2022Ordinal Causal Discoverycited by 6
  6. 2025Permutation-Based Rank Test in the Presence of Discretization and Application in Causal Discovery with Mixed Datacited by 5
  7. 2020Learning Bayesian Networks from Ordinal Datacited by 4
  8. 2026Discrete Causal Representation Learningcited by 3
  9. 2026Score-Based Causal Discovery of Latent Variable Causal Modelscited by 3
  10. 2019Learning Attribute Patterns in High-Dimensional Structured Latent Attribute Modelscited by 2
  11. 2021Learning and scoring Gaussian latent variable causal models with unknown additive interventionscited by 2
  12. 2021Inference for a Large Directed Acyclic Graph with Unspecified Interventionscited by 2
  13. 2023Latent Conjunctive Bayesian Network: Unify Attribute Hierarchy and Bayesian Network for Cognitive Diagnosiscited by 2
  14. 2023Causal Discovery with Generalized Linear Models through Peeling Algorithmscited by 2
  15. 2023Learning Bayesian networks: a copula approach for mixed-type datacited by 2
  16. 2025Score-based Greedy Search for Structure Identification of Partially Observed Linear Causal Modelscited by 2
  17. 2026Beyond Vintage Rotation: Bias-Free Sparse Representation Learning with Oracle Inferencecited by 2
  18. 2023When Composite Likelihood Meets Stochastic Approximationcited by 1

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