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Counterfactual Probabilities: Computational Methods, Bounds and Applications

arXiv 1302.6784 ↗First posted 27 Feb 2013cs.AIcited by 67

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Abstract (arXiv)

Evaluation of counterfactual queries (e.g., "If A were true, would C have been true?") is important to fault diagnosis, planning, and determination of liability. In this paper we present methods for computing the probabilities of such queries using the formulation proposed in [Balke and Pearl, 1994], where the antecedent of the query is interpreted as an external action that forces the proposition A to be true. When a prior probability is available on the causal mechanisms governing the domain, counterfactual probabilities can be evaluated precisely. However, when causal knowledge is specified as conditional probabilities on the observables, only bounds can computed. This paper develops techniques for evaluating these bounds, and demonstrates their use in two applications: (1) the determination of treatment efficacy from studies in which subjects may choose their own treatment, and (2) the determination of liability in product-safety litigation.

Key facts. Cited by 67 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 Feb 2013.

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Citing papers per year: 2020: 1; 2021: 8; 2022: 15; 2023: 10; 2024: 8; 2025: 10; 2026: 15.

67 papers.

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  1. 2021The Causal-Neural Connection: Expressiveness, Learnability, and Inferencecited by 97
  2. 2021Partial Counterfactual Identification from Observational and Experimental Datacited by 64
  3. 2023Counterfactual Identifiability of Bijective Causal Modelscited by 42
  4. 2021An Automated Approach to Causal Inference in Discrete Settingscited by 39
  5. 2021Instrumental Variable Value Iteration for Causal Offline Reinforcement Learningcited by 35
  6. 2022Counterfactual harmcited by 29
  7. 2022Causal Imitation Learning under Temporally Correlated Noisecited by 28
  8. 2022Stochastic Causal Programming for Bounding Treatment Effectscited by 25
  9. 2022Causal Inference Through the Structural Causal Marginal Problemcited by 22
  10. 2024Counterfactual Image Editingcited by 20
  11. 2024Root Cause Analysis of Outliers with Missing Structural Knowledgecited by 19
  12. 2025Causally Reliable Concept Bottleneck Modelscited by 17
38 more
  1. 2022Filtered-CoPhy: Unsupervised Learning of Counterfactual Physics in Pixel Spacecited by 14
  2. 2023Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Modelcited by 14
  3. 2022Detecting hidden confounding in observational data using multiple environmentscited by 13
  4. 2021Safe Policy Learning through Extrapolation: Application to Pre-trial Risk Assessmentcited by 10
  5. 2022Partial Identification with Noisy Covariates: A Robust Optimization Approachcited by 10
  6. 2022Counterfactual Analysis in Dynamic Latent State Modelscited by 9
  7. 2022Causal Inference with Treatment Measurement Error: A Nonparametric Instrumental Variable Approachcited by 9
  8. 2023Approximating Counterfactual Bounds while Fusing Observational, Biased and Randomised Data Sourcescited by 9
  9. 2020Causal Transfer for Imitation Learning and Decision Making under Sensor-shiftcited by 8
  10. 2021Neural Networks for Learning Counterfactual G-Invariances from Single Environmentscited by 8
  11. 2023Causal Fairness for Outcome Controlcited by 8
  12. 2023Efficient Computation of Counterfactual Boundscited by 8
  13. 2022On the Complexity of Counterfactual Reasoningcited by 7
  14. 2023Scalable Computation of Causal Boundscited by 5
  15. 2026Do Language Models Track Entities Across State Changes?cited by 5
  16. 2023Results on Counterfactual Invariancecited by 4
  17. 2024Causal Inference with Latent Variables: Recent Advances and Future Prospectivescited by 4
  18. 2024Learning Representations of Instruments for Partial Identification of Treatment Effectscited by 4
  19. 2021SBI: A Simulation-Based Test of Identifiability for Bayesian Causal Inferencecited by 3
  20. 2022The Causal Marginal Polytope for Bounding Treatment Effectscited by 3
  21. 2022Explaining the root causes of unit-level changescited by 3
  22. 2022Partial counterfactual identification and uplift modeling: theoretical results and real-world assessmentcited by 3
  23. 2023Bounding probabilities of causation through the causal marginal problemcited by 3
  24. 2023Learning with Selectively Labeled Data from Multiple Decision-makerscited by 3
  25. 2024Consistency of Neural Causal Partial Identificationcited by 3
  26. 2021Algorithmic Recourse in Partially and Fully Confounded Settings Through Bounding Counterfactual Effectscited by 2
  27. 2024Nondeterministic Causal Modelscited by 2
  28. 2025Robust Counterfactual Inference in Markov Decision Processescited by 2
  29. 2025Multilinear and Linear Programs for Partially Identifiable Queries in Quasi-Markovian Structural Causal Modelscited by 2
  30. 2026Information-Theoretic Causal Bounds under Unmeasured Confoundingcited by 2
  31. 2026IV-ICL: Bounding Causal Effects with Instrumental Variables via In-Context Learningcited by 2
  32. 2026Foundation Models for Partial Causal Identificationcited by 2
  33. 2023Tightening Bounds on Probabilities of Causation By Merging Datasetscited by 1
  34. 2024Do No Harm: A Counterfactual Approach to Safe Reinforcement Learningcited by 1
  35. 2025Causal Imitation Learning under Expert-Observable and Expert-Unobservable Confoundingcited by 1
  36. 2025Counterfactual Strategies for Markov Decision Processescited by 1
  37. 2025Causal Counterfactuals Reconsideredcited by 1
  38. 2026Statistical Inference and Learning for Shapley Additive Explanations (SHAP)cited by 1

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