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Probabilities of Causation: Bounds and Identification

arXiv 1301.3898 ↗First posted 16 Jan 2013cs.AIcited by 89

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Abstract (arXiv)

This paper deals with the problem of estimating the probability that one event was a cause of another in a given scenario. Using structural-semantical definitions of the probabilities of necessary or sufficient causation (or both), we show how to optimally bound these quantities from data obtained in experimental and observational studies, making minimal assumptions concerning the data-generating process. In particular, we strengthen the results of Pearl (1999) by weakening the data-generation assumptions and deriving theoretically sharp bounds on the probabilities of causation. These results delineate precisely how empirical data can be used both in settling questions of attribution and in solving attribution-related problems of decision making.

Key facts. Cited by 89 papers in the map (data through 7 Oct 2026). First posted on arXiv 16 Jan 2013.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 10; 2022: 12; 2023: 16; 2024: 10; 2025: 14; 2026: 27.

89 papers.

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  1. 2021Desiderata for Representation Learning: A Causal Perspectivecited by 76
  2. 2021Partial Counterfactual Identification from Observational and Experimental Datacited by 64
  3. 2021Explaining Black-Box Algorithms Using Probabilistic Contrastive Counterfactualscited by 55
  4. 2021Local Explanations via Necessity and Sufficiency: Unifying Theory and Practicecited by 45
  5. 2023Counterfactual Identifiability of Bijective Causal Modelscited by 42
  6. 2021Causes of Effects: Learning individual responses from population datacited by 36
  7. 2022Counterfactual harmcited by 29
  8. 2022Personalized Decision Making -- A Conceptual Introductioncited by 29
  9. 2024Causal Concept Graph Models: Beyond Causal Opacity in Deep Learningcited by 28
  10. 2022Probabilities of Causation with Nonbinary Treatment and Effectcited by 24
  11. 2021Bounds on Causal Effects and Application to High Dimensional Datacited by 22
  12. 2022Causal Inference Through the Structural Causal Marginal Problemcited by 22
38 more
  1. 2021Estimating Categorical Counterfactuals via Deep Twin Networkscited by 18
  2. 2021Unit Selection with Causal Diagramcited by 17
  3. 2023On Learning Necessary and Sufficient Causal Graphscited by 14
  4. 2023Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Modelcited by 14
  5. 2022On the Probability of Necessity and Sufficiency of Explaining Graph Neural Networks: A Lower Bound Optimization Approachcited by 11
  6. 2021A Topological Perspective on Causal Inferencecited by 10
  7. 2022Counterfactual Analysis in Dynamic Latent State Modelscited by 9
  8. 2023Approximating Counterfactual Bounds while Fusing Observational, Biased and Randomised Data Sourcescited by 9
  9. 2022Probabilities of Causation: Adequate Size of Experimental and Observational Samplescited by 8
  10. 2022On the Complexity of Counterfactual Reasoningcited by 7
  11. 2023Reconciling Predictive and Statistical Parity: A Causal Approachcited by 7
  12. 2025Confounding Robust Deep Reinforcement Learning: A Causal Approachcited by 6
  13. 2022Unit Selection: Case Study and Comparison with A/B Test Heuristiccited by 5
  14. 2022Probabilities of Causation: Role of Observational Datacited by 5
  15. 2025Counterfactual Identifiability via Dynamic Optimal Transportcited by 5
  16. 2023Epsilon-Identifiability of Causal Quantitiescited by 4
  17. 2025CausalARC: Abstract Reasoning with Causal World Modelscited by 4
  18. 2021SBI: A Simulation-Based Test of Identifiability for Bayesian Causal Inferencecited by 3
  19. 2022Partial counterfactual identification and uplift modeling: theoretical results and real-world assessmentcited by 3
  20. 2023Bounding probabilities of causation through the causal marginal problemcited by 3
  21. 2023Approximate Causal Effect Identification under Weak Confoundingcited by 3
  22. 2024Unifying Invariance and Spuriousity for Graph Out-of-Distribution via Probability of Necessity and Sufficiencycited by 3
  23. 2025The Limits of Predicting Agents from Behaviourcited by 3
  24. 2022Risk-Averse Multi-Armed Bandits with Unobserved Confounders: A Case Study in Emotion Regulation in Mobile Healthcited by 2
  25. 2023Bounding the Probabilities of Benefit and Harm Through Sensitivity Parameters and Proxiescited by 2
  26. 2024Unifying Invariant and Variant Features for Graph Out-of-Distribution via Probability of Necessity and Sufficiencycited by 2
  27. 2024GIFT: A Framework Towards Global Interpretable Faithful Textual Explanations of Vision Classifierscited by 2
  28. 2025Estimating Probabilities of Causation with Machine Learning Modelscited by 2
  29. 2025Abstract Counterfactuals for Language Model Agentscited by 2
  30. 2025Multilinear and Linear Programs for Partially Identifiable Queries in Quasi-Markovian Structural Causal Modelscited by 2
  31. 2026Information-Theoretic Causal Bounds under Unmeasured Confoundingcited by 2
  32. 2026Causal Evaluation of Membership Inference Attackscited by 2
  33. 2026IV-ICL: Bounding Causal Effects with Instrumental Variables via In-Context Learningcited by 2
  34. 2026Foundation Models for Partial Causal Identificationcited by 2
  35. 2023An Algorithm and Complexity Results for Causal Unit Selectioncited by 1
  36. 2023Tightening Bounds on Probabilities of Causation By Merging Datasetscited by 1
  37. 2024Bayesian Networks for Causal Analysis in Socioecological Systemscited by 1
  38. 2025Identification of Probabilities of Causation: from Recursive to Closed-Form Boundscited by 1

50 most cited of 89 All 89 (JSON)