mlsanityData to 14 Oct 2026

Nested Counterfactual Identification from Arbitrary Surrogate Experiments

arXiv 2107.03190 ↗First posted 7 Jul 2021cs.AI cs.LG stat.MEcited by 38

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Abstract (arXiv)

The Ladder of Causation describes three qualitatively different types of activities an agent may be interested in engaging in, namely, seeing (observational), doing (interventional), and imagining (counterfactual) (Pearl and Mackenzie, 2018). The inferential challenge imposed by the causal hierarchy is that data is collected by an agent observing or intervening in a system (layers 1 and 2), while its goal may be to understand what would have happened had it taken a different course of action, contrary to what factually ended up happening (layer 3). While there exists a solid understanding of the conditions under which cross-layer inferences are allowed from observations to interventions, the results are somewhat scarcer when targeting counterfactual quantities. In this paper, we study the identification of nested counterfactuals from an arbitrary combination of observations and experiments. Specifically, building on a more explicit definition of nested counterfactuals, we prove the counterfactual unnesting theorem (CUT), which allows one to map arbitrary nested counterfactuals to unnested ones. For instance, applications in mediation and fairness analysis usually evoke notions of direct, indirect, and spurious effects, which naturally require nesting. Second, we introduce a sufficient and necessary graphical condition for counterfactual identification from an arbitrary combination of observational and experimental distributions. Lastly, we develop an efficient and complete algorithm for identifying nested counterfactuals; failure of the algorithm returning an expression for a query implies it is not identifiable.

Key facts. Cited by 38 papers in the map (data through 14 Oct 2026). Builds on 5 of its 30 references that are in the map. First posted on arXiv 7 Jul 2021.

Builds on

5 of 30 references.

References · 5

  1. 2013Direct and Indirect Effectscited by 280
  2. 2013Probabilistic Evaluation of Sequential Plans from Causal Models with Hidden Variablescited by 24
  3. 2013A Probabilistic Calculus of Actionscited by 14
  4. 2013Testing Identifiability of Causal Effectscited by 8
  5. 2014Statistical Causality from a Decision-Theoretic Perspectivecited by 7

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 1; 2022: 6; 2023: 12; 2024: 6; 2025: 7; 2026: 6.

38 papers.

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  1. 2021Partial Counterfactual Identification from Observational and Experimental Datacited by 64
  2. 2022Neural Causal Models for Counterfactual Identification and Estimationcited by 57
  3. 2023Counterfactual Identifiability of Bijective Causal Modelscited by 43
  4. 2022Causal Effect Identification in Cluster DAGscited by 36
  5. 2023Discovering Causal Relations and Equations from Datacited by 36
  6. 2023Sharp Bounds for Generalized Causal Sensitivity Analysiscited by 24
  7. 2022Causal Inference Through the Structural Causal Marginal Problemcited by 23
  8. 2024Counterfactual Image Editingcited by 20
  9. 2023Counterfactual (Non-)identifiability of Learned Structural Causal Modelscited by 17
  10. 2023Causal models in string diagramscited by 14
  11. 2023Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Modelcited by 14
  12. 2023Finding Counterfactually Optimal Action Sequences in Continuous State Spacescited by 13
26 more
  1. 2022Disentangling Causal Effects from Sets of Interventions in the Presence of Unobserved Confounderscited by 10
  2. 2023Causal Fairness under Unobserved Confounding: A Neural Sensitivity Frameworkcited by 10
  3. 2024Modular Learning of Deep Causal Generative Models for High-dimensional Causal Inferencecited by 9
  4. 2022On the Complexity of Counterfactual Reasoningcited by 7
  5. 2025Counterfactual Identifiability via Dynamic Optimal Transportcited by 6
  6. 2023On Identifiability of Conditional Causal Effectscited by 4
  7. 2024Counterfactual Effect Decomposition in Multi-Agent Sequential Decision Makingcited by 4
  8. 2022Partial counterfactual identification and uplift modeling: theoretical results and real-world assessmentcited by 3
  9. 2023s-ID: Causal Effect Identification in a Sub-Populationcited by 3
  10. 2025Path-specific effects for pulse-oximetry guided decisions in critical carecited by 2
  11. 2026Computational Identifiabilitycited by 2
  12. 2023Simulating counterfactualscited by 1
  13. 2023Agent-Specific Effects: A Causal Effect Propagation Analysis in Multi-Agent MDPscited by 1
  14. 2024Bayesian Networks for Causal Analysis in Socioecological Systemscited by 1
  15. 2024Causal Effect Identification in a Sub-Population with Latent Variablescited by 1
  16. 2024Teleporter Theory: A General and Simple Approach for Modeling Cross-World Counterfactual Causalitycited by 0
  17. 2025Learning Counterfactual Outcomes Under Rank Preservationcited by 0
  18. 2025DISCO: Mitigating Bias in Deep Learning with Conditional Distance Correlationcited by 0
  19. 2025Causal identification with Y0cited by 0
  20. 2025On Predicting Post-Click Conversion Rate via Counterfactual Inferencecited by 0
  21. 2025From Black-box to Causal-box: Towards Building More Interpretable Modelscited by 0
  22. 2026Estimating Causal Effects in Gaussian Linear SCMs with Finite Datacited by 0
  23. 2026Automatic Causal Fairness Analysis with LLM-Generated Reportingcited by 0
  24. 2026Shadow-Loom: Causal Reasoning over Graphical World Models of Narrativescited by 0
  25. 2026Causal Algorithmic Recourse: Foundations and Methodscited by 0
  26. 2026Partial Identification under Causal Orders by Linear Programmingcited by 0