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Directed Cyclic Graphical Representations of Feedback Models

arXiv 1302.4982 ↗First posted 20 Feb 2013cs.AIcited by 27

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Abstract (arXiv)

The use of directed acyclic graphs (DAGs) to represent conditional independence relations among random variables has proved fruitful in a variety of ways. Recursive structural equation models are one kind of DAG model. However, non-recursive structural equation models of the kinds used to model economic processes are naturally represented by directed cyclic graphs with independent errors, a characterization of conditional independence errors, a characterization of conditional independence constraints is obtained, and it is shown that the result generalizes in a natural way to systems in which the error variables or noises are statistically dependent. For non-linear systems with independent errors a sufficient condition for conditional independence of variables in associated distributions is obtained.

Key facts. Cited by 27 papers in the map (data through 7 Oct 2026). First posted on arXiv 20 Feb 2013.

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Citing papers per year: 2021: 2; 2022: 5; 2023: 6; 2024: 5; 2025: 4; 2026: 5.

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  1. 2022Deep End-to-end Causal Inferencecited by 93
  2. 2023A Survey on Causal Discovery: Theory and Practicecited by 63
  3. 2022What-is and How-to for Fairness in Machine Learning: A Survey, Reflection, and Perspectivecited by 18
  4. 2021Dynamic Causal Bayesian Optimizationcited by 17
  5. 2023Causal Discovery from Time Series with Hybrids of Constraint-Based and Noise-Based Algorithmscited by 8
  6. 2024Local Causal Discovery with Linear non-Gaussian Cyclic Modelscited by 7
  7. 2022Learning Relational Causal Models with Cycles through Relational Acyclificationcited by 6
  8. 2023Establishing Markov Equivalence in Cyclic Directed Graphscited by 5
  9. 2021Causality and independence in perfectly adapted dynamical systemscited by 4
  10. 2022Relational Causal Models with Cycles:Representation and Reasoningcited by 4
  11. 2025Differentiable Cyclic Causal Discovery Under Unmeasured Confounderscited by 4
  12. 2023Procedural Fairness Through Decoupling Objectionable Data Generating Componentscited by 3
15 more
  1. 2024Interventional Causal Discovery in a Mixture of DAGscited by 3
  2. 2025Causal Discovery via Quantile Partial Effectcited by 3
  3. 2023On the Foundations of Cycles in Bayesian Networkscited by 2
  4. 2026Coarsening Linear Non-Gaussian Causal Models with Cyclescited by 2
  5. 2026DAG-FM: A Foundation Model for Causal Discovery under Heterogeneous Causal Mechanismscited by 2
  6. 2022Identifying Unique Spatial-Temporal Bayesian Network without Markov Equivalencecited by 1
  7. 2023Markov Conditions and Factorization in Logical Credal Networkscited by 1
  8. 2025Lower Bounds on the Size of Markov Equivalence Classescited by 1
  9. 2024DIGIC: Domain Generalizable Imitation Learning by Causal Discoverycited by 0
  10. 2024Spatio-Temporal Graphical Counterfactuals: An Overviewcited by 0
  11. 2024Robust Causal Analysis of Linear Cyclic Systems With Hidden Confounderscited by 0
  12. 2025σ-Maximal Ancestral Graphscited by 0
  13. 2026SCOUT: Cyclic Causal Discovery Under Soft Interventions with Unknown Targetscited by 0
  14. 2026Beyond Directed Acyclic Graphs: Causal Zeros and Causal Differential Equationscited by 0
  15. 2026Causal Reasoning with Bipartite Graphical Causal Modelscited by 0