mlsanityData to 7 Oct 2026

Foundations of Structural Causal Models with Cycles and Latent Variables

arXiv 1611.06221 ↗First posted 18 Nov 2016stat.ME cs.AI cs.LGcited by 134

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Abstract (arXiv)

Structural causal models (SCMs), also known as (nonparametric) structural equation models (SEMs), are widely used for causal modeling purposes. In particular, acyclic SCMs, also known as recursive SEMs, form a well-studied subclass of SCMs that generalize causal Bayesian networks to allow for latent confounders. In this paper, we investigate SCMs in a more general setting, allowing for the presence of both latent confounders and cycles. We show that in the presence of cycles, many of the convenient properties of acyclic SCMs do not hold in general: they do not always have a solution; they do not always induce unique observational, interventional and counterfactual distributions; a marginalization does not always exist, and if it exists the marginal model does not always respect the latent projection; they do not always satisfy a Markov property; and their graphs are not always consistent with their causal semantics. We prove that for SCMs in general each of these properties does hold under certain solvability conditions. Our work generalizes results for SCMs with cycles that were only known for certain special cases so far. We introduce the class of simple SCMs that extends the class of acyclic SCMs to the cyclic setting, while preserving many of the convenient properties of acyclic SCMs. With this paper we aim to provide the foundations for a general theory of statistical causal modeling with SCMs.

Key facts. Cited by 134 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Nov 2016.

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Citing papers per year: 2021: 10; 2022: 22; 2023: 30; 2024: 22; 2025: 27; 2026: 23.

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  11. 2023BayesDAG: Gradient-Based Posterior Inference for Causal Discoverycited by 33
  12. 2021Compositional Abstraction Error and a Category of Causal Modelscited by 32
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  25. 2022Identifying Causal Effects using Instrumental Time Series: Nuisance IV and Correcting for the Pastcited by 9
  26. 2022Identifiability of Sparse Causal Effects using Instrumental Variablescited by 9
  27. 2024Separation-based distance measures for causal graphscited by 9
  28. 2024Learning Causal Abstractions of Linear Structural Causal Modelscited by 9
  29. 2023A Measure-Theoretic Axiomatisation of Causalitycited by 8
  30. 2026From Zero to Hero: Advancing Zero-Shot Foundation Models for Tabular Outlier Detectioncited by 8
  31. 2022A Unified Experiment Design Approach for Cyclic and Acyclic Causal Modelscited by 7
  32. 2023Intervention Generalization: A View from Factor Graph Modelscited by 7
  33. 2024A Fixed-Point Approach for Causal Generative Modelingcited by 7
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  36. 2022Learning Relational Causal Models with Cycles through Relational Acyclificationcited by 6
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  38. 2024Are Bayesian networks typically faithful?cited by 6

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