mlsanityData to 7 Oct 2026

Probabilities of Causation for Continuous and Vector Variables

arXiv 2405.20487 ↗First posted 30 May 2024cs.AIcited by 8

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Abstract (arXiv)

Probabilities of causation (PoC) are valuable concepts for explainable artificial intelligence and practical decision-making. PoC are originally defined for scalar binary variables. In this paper, we extend the concept of PoC to continuous treatment and outcome variables, and further generalize PoC to capture causal effects between multiple treatments and multiple outcomes. In addition, we consider PoC for a sub-population and PoC with multi-hypothetical terms to capture more sophisticated counterfactual information useful for decision-making. We provide a nonparametric identification theorem for each type of PoC we introduce. Finally, we illustrate the application of our results on a real-world dataset about education.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 17 of its 53 references that are in the map. First posted on arXiv 30 May 2024.

Builds on

17 of 53 references.

References · 17

  1. 2019Kernel Instrumental Variable Regressioncited by 118
  2. 2020Learning Deep Features in Instrumental Variable Regressioncited by 65
  3. 2015Nonparametric methods for doubly robust estimation of continuous treatment effectscited by 62
  4. 2018Policy Evaluation and Optimization with Continuous Treatmentscited by 57
  5. 2021Explaining Black-Box Algorithms Using Probabilistic Contrastive Counterfactualscited by 55
  6. 2021Local Explanations via Necessity and Sufficiency: Unifying Theory and Practicecited by 45
  7. 2019Contextual Bandits with Continuous Actions: Smoothing, Zooming, and Adaptingcited by 42
  8. 2021Causes of Effects: Learning individual responses from population datacited by 36
  9. 2020Efficient Contextual Bandits with Continuous Actionscited by 24
  10. 2022Probabilities of Causation with Nonbinary Treatment and Effectcited by 24
  11. 2021Unit Selection with Causal Diagramcited by 17
  12. 2022Unit Selection with Nonbinary Treatment and Effectcited by 12
5 more
  1. 2021End-to-End Balancing for Causal Continuous Treatment-Effect Estimationcited by 9
  2. 2016Estimating scaled treatment effects with multiple outcomescited by 7
  3. 2022Probabilities of Causation: Role of Observational Datacited by 5
  4. 2014Bounding the Probability of Causation in Mediation Analysiscited by 4
  5. 2013From Statistical Evidence to Evidence of Causalitycited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 2; 2026: 4.

8 papers.

  1. 2025Moments of Causal Effectscited by 3
  2. 2025Decomposition of Probabilities of Causation with Two Mediatorscited by 2
  3. 2024Mediation Analysis for Probabilities of Causationcited by 1
  4. 2026Bounds and Identification of Joint Probabilities of Potential Outcomes and Observed Variables under Monotonicity Assumptionscited by 1
  5. 2024Removing Spurious Correlation from Neural Network Interpretationscited by 0
  6. 2026Preference-based Conditional Treatment Effects and Policy Learningcited by 0
  7. 2026Causal EpiNets: Precision-corrected Bounds on Individual Treatment Effects using Epistemic Neural Networkscited by 0
  8. 2026Partial Identification under Causal Orders by Linear Programmingcited by 0