mlsanityData to 14 Oct 2026

Recursive Causal Structure Learning in the Presence of Latent Variables and Selection Bias

arXiv 2110.12036 ↗First posted 22 Oct 2021cs.LGcited by 29

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Abstract (arXiv)

We consider the problem of learning the causal MAG of a system from observational data in the presence of latent variables and selection bias. Constraint-based methods are one of the main approaches for solving this problem, but the existing methods are either computationally impractical when dealing with large graphs or lacking completeness guarantees. We propose a novel computationally efficient recursive constraint-based method that is sound and complete. The key idea of our approach is that at each iteration a specific type of variable is identified and removed. This allows us to learn the structure efficiently and recursively, as this technique reduces both the number of required conditional independence (CI) tests and the size of the conditioning sets. The former substantially reduces the computational complexity, while the latter results in more reliable CI tests. We provide an upper bound on the number of required CI tests in the worst case. To the best of our knowledge, this is the tightest bound in the literature. We further provide a lower bound on the number of CI tests required by any constraint-based method. The upper bound of our proposed approach and the lower bound at most differ by a factor equal to the number of variables in the worst case. We provide experimental results to compare the proposed approach with the state of the art on both synthetic and real-world structures.

Key facts. Cited by 29 papers in the map (data through 14 Oct 2026). Builds on 6 of its 35 references that are in the map. First posted on arXiv 22 Oct 2021.

Builds on

6 of 35 references.

References · 6

  1. 2015Doubly Robust Off-policy Value Evaluation for Reinforcement Learningcited by 339
  2. 2016Data-Efficient Off-Policy Policy Evaluation for Reinforcement Learningcited by 286
  3. 2013Learning Sparse Causal Models is not NP-hardcited by 49
  4. 2020A Recursive Markov Boundary-Based Approach to Causal Structure Learningcited by 21
  5. 2018A Constraint-Based Algorithm For Causal Discovery with Cycles, Latent Variables and Selection Biascited by 16
  6. 2020Bayesian network structure learning with causal effects in the presence of latent variablescited by 8

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 6; 2023: 7; 2024: 5; 2025: 4; 2026: 7.

29 papers.

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  1. 2022Latent Hierarchical Causal Structure Discovery with Rank Constraintscited by 51
  2. 2023A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variablescited by 33
  3. 2023Identification of Nonlinear Latent Hierarchical Modelscited by 27
  4. 2024Recursive Causal Discoverycited by 12
  5. 2024Local Causal Structure Learning in the Presence of Latent Variablescited by 11
  6. 2022Novel Ordering-based Approaches for Causal Structure Learning in the Presence of Unobserved Variablescited by 10
  7. 2022A Unified Experiment Design Approach for Cyclic and Acyclic Causal Modelscited by 7
  8. 2024On the Parameter Identifiability of Partially Observed Linear Causal Modelscited by 7
  9. 2024A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discoverycited by 7
  10. 2023Causal Imitability Under Context-Specific Independence Relationscited by 6
  11. 2025Efficient Ensemble Conditional Independence Test Framework for Causal Discoverycited by 5
  12. 2022Causal Effect Identification in Uncertain Causal Networkscited by 3
17 more
  1. 2023s-ID: Causal Effect Identification in a Sub-Populationcited by 3
  2. 2024Differentiable Causal Discovery For Latent Hierarchical Causal Modelscited by 3
  3. 2026Score-Based Causal Discovery of Latent Variable Causal Modelscited by 3
  4. 2022Experimental Design for Causal Effect Identificationcited by 2
  5. 2022GT-CausIn: a novel causal-based insight for traffic predictioncited by 2
  6. 2025Score-based Greedy Search for Structure Identification of Partially Observed Linear Causal Modelscited by 2
  7. 2023A Review and Roadmap of Deep Causal Model from Different Causal Structures and Representationscited by 1
  8. 2023On the Three Demons in Causality in Finance: Time Resolution, Nonstationarity, and Latent Factorscited by 1
  9. 2026Traceable Latent Variable Discovery Based on Multi-Agent Collaborationcited by 1
  10. 2026Consistency evaluation of benchmarks used for causal discoverycited by 1
  11. 2023Learning Linear Gaussian Polytree Models with Interventionscited by 0
  12. 2025A Critical Review of Predominant Bias in Neural Networkscited by 0
  13. 2025Uncovering Bias Mechanisms in Observational Studiescited by 0
  14. 2026A Recursive Decomposition Framework for Causal Structure Learning in the Presence of Latent Variablescited by 0
  15. 2026Causal Modeling of Selection in Evolutioncited by 0
  16. 2026Decoupled Causal Discoverycited by 0
  17. 2026Hessian Rank Constraint for Learning Structure of Nonlinear Latent Variable Modelscited by 0