mlsanityData to 7 Oct 2026

Probabilities of Causation with Nonbinary Treatment and Effect

arXiv 2208.09568 ↗First posted 19 Aug 2022cs.AIcited by 24

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Abstract (arXiv)

This paper deals with the problem of estimating the probabilities of causation when treatment and effect are not binary. Tian and Pearl derived sharp bounds for the probability of necessity and sufficiency (PNS), the probability of sufficiency (PS), and the probability of necessity (PN) using experimental and observational data. In this paper, we provide theoretical bounds for all types of probabilities of causation to multivalued treatments and effects. We further discuss examples where our bounds guide practical decisions and use simulation studies to evaluate how informative the bounds are for various combinations of data.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). Builds on 5 of its 13 references that are in the map. First posted on arXiv 19 Aug 2022.

Builds on

5 of 13 references.

References · 5

  1. 2013Probabilities of Causation: Bounds and Identificationcited by 89
  2. 2021Partial Counterfactual Identification from Observational and Experimental Datacited by 64
  3. 2021Causes of Effects: Learning individual responses from population datacited by 36
  4. 2021Bounds on Causal Effects and Application to High Dimensional Datacited by 22
  5. 2021Unit Selection with Causal Diagramcited by 17

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Cited by year (2026 to 7 Oct)

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

24 papers.

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  1. 2023Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Modelcited by 14
  2. 2022Unit Selection with Nonbinary Treatment and Effectcited by 12
  3. 2022Probabilities of Causation: Adequate Size of Experimental and Observational Samplescited by 8
  4. 2024Probabilities of Causation for Continuous and Vector Variablescited by 8
  5. 2022Unit Selection: Learning Benefit Function from Finite Population Datacited by 6
  6. 2022Unit Selection: Case Study and Comparison with A/B Test Heuristiccited by 5
  7. 2022Probabilities of Causation: Role of Observational Datacited by 5
  8. 2023Epsilon-Identifiability of Causal Quantitiescited by 4
  9. 2023Bounding probabilities of causation through the causal marginal problemcited by 3
  10. 2025Moments of Causal Effectscited by 3
  11. 2023Bounding the Probabilities of Benefit and Harm Through Sensitivity Parameters and Proxiescited by 2
  12. 2024Unifying Invariant and Variant Features for Graph Out-of-Distribution via Probability of Necessity and Sufficiencycited by 2
12 more
  1. 2025Estimating Probabilities of Causation with Machine Learning Modelscited by 2
  2. 2025Decomposition of Probabilities of Causation with Two Mediatorscited by 2
  3. 2025Statistical Decision Theory with Counterfactual Losscited by 2
  4. 2023Tightening Bounds on Probabilities of Causation By Merging Datasetscited by 1
  5. 2025Identification of Probabilities of Causation: from Recursive to Closed-Form Boundscited by 1
  6. 2025Learning Probabilities of Causation with Mask-Augmented Datacited by 1
  7. 2026Bounds and Identification of Joint Probabilities of Potential Outcomes and Observed Variables under Monotonicity Assumptionscited by 1
  8. 2023Causality-Based Feature Importance Quantifying Methods: PN-FI, PS-FI and PNS-FIcited by 0
  9. 2026Preference-based Conditional Treatment Effects and Policy Learningcited by 0
  10. 2026Bounding Probabilities of Causation with Partial Causal Diagramscited by 0
  11. 2026General sample size analysis for probabilities of causation: a delta method approachcited by 0
  12. 2026Causal EpiNets: Precision-corrected Bounds on Individual Treatment Effects using Epistemic Neural Networkscited by 0