mlsanityData to 14 Oct 2026

Generalized Independent Noise Condition for Estimating Causal Structure with Latent Variables

arXiv 2308.06718 ↗First posted 13 Aug 2023cs.LG cs.AI stat.MEcited by 11

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Abstract (arXiv)

We investigate the task of learning causal structure in the presence of latent variables, including locating latent variables and determining their quantity, and identifying causal relationships among both latent and observed variables. To this end, we propose a Generalized Independent Noise (GIN) condition for linear non-Gaussian acyclic causal models that incorporate latent variables, which establishes the independence between a linear combination of certain measured variables and some other measured variables. Specifically, for two observed random vectors bfY and bfZ, GIN holds if and only if ωintercalY and Z are independent, where ω is a non-zero parameter vector determined by the cross-covariance between Y and Z. We then give necessary and sufficient graphical criteria of the GIN condition in linear non-Gaussian acyclic models. Roughly speaking, GIN implies the existence of a set S such that S is causally earlier (w.r.t. the causal ordering) than Y, and that every active (collider-free) path between Y and Z must contain a node from S. Interestingly, we find that the independent noise condition (i.e., if there is no confounder, causes are independent of the residual derived from regressing the effect on the causes) can be seen as a special case of GIN. With such a connection between GIN and latent causal structures, we further leverage the proposed GIN condition, together with a well-designed search procedure, to efficiently estimate Linear, Non-Gaussian Latent Hierarchical Models (LiNGLaHs), where latent confounders may also be causally related and may even follow a hierarchical structure. We show that the causal structure of a LiNGLaH is identifiable in light of GIN conditions. Experimental results show the effectiveness of the proposed method.

Key facts. Cited by 11 papers in the map (data through 14 Oct 2026). Builds on 13 of its 64 references that are in the map. First posted on arXiv 13 Aug 2023.

Builds on

13 of 64 references.

References · 13

  1. 2013Causal Discovery with Continuous Additive Noise Modelscited by 255
  2. 2013Causal Inference in the Presence of Latent Variables and Selection Biascited by 166
  3. 2013Learning Sparse Causal Models is not NP-hardcited by 49
  4. 2019Learning Linear Non-Gaussian Causal Models in the Presence of Latent Variablescited by 39
  5. 2016Large-Scale Kernel Methods for Independence Testingcited by 32
  6. 2013ParceLiNGAM: A causal ordering method robust against latent confounderscited by 29
  7. 2020Causal Discovery with Unobserved Confounding and non-Gaussian Datacited by 25
  8. 2017Robust causal structure learning with some hidden variablescited by 17
  9. 2013Calculation of Entailed Rank Constraints in Partially Non-Linear and Cyclic Modelscited by 12
  10. 2014Marginal likelihood and model selection for Gaussian latent tree and forest modelscited by 12
  11. 2021Temporal-Spatial Causal Interpretations for Vision-Based Reinforcement Learningcited by 6
  12. 2014A Survey on Latent Tree Models and Applicationscited by 5
1 more
  1. 2016Latent Tree Analysiscited by 3

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 2; 2025: 6; 2026: 3.

11 papers.

  1. 2025Unveiling and Causalizing CoT: A Causal Pespectivecited by 6
  2. 2024Parameter identification in linear non-Gaussian causal models under general confoundingcited by 5
  3. 2025The Third Pillar of Causal Analysis? A Measurement Perspective on Causal Representationscited by 4
  4. 2026Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learningcited by 4
  5. 2024Automating the Selection of Proxy Variables of Unmeasured Confounderscited by 2
  6. 2025Deep Discrete Encoders: Identifiable Deep Generative Models for Rich Data with Discrete Latent Layerscited by 2
  7. 2025On Theoretical Identifiability of Discrete Latent Causal Graphical Modelscited by 0
  8. 2025Position: Beyond Sensitive Attributes, ML Fairness Should Quantify Structural Injustice via Social Determinantscited by 0
  9. 2025Linear Causal Representation Learning by Topological Ordering, Pruning, and Disentanglementcited by 0
  10. 2026Iterative Identification Closure: Amplifying Causal Identifiability in Linear SEMscited by 0
  11. 2026A Recursive Decomposition Framework for Causal Structure Learning in the Presence of Latent Variablescited by 0