mlsanityData to 14 Oct 2026

Approximating Counterfactual Bounds while Fusing Observational, Biased and Randomised Data Sources

arXiv 2307.16577 ↗First posted 31 Jul 2023stat.ME cs.AIcited by 9

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Abstract (arXiv)

We address the problem of integrating data from multiple, possibly biased, observational and interventional studies, to eventually compute counterfactuals in structural causal models. We start from the case of a single observational dataset affected by a selection bias. We show that the likelihood of the available data has no local maxima. This enables us to use the causal expectation-maximisation scheme to approximate the bounds for partially identifiable counterfactual queries, which are the focus of this paper. We then show how the same approach can address the general case of multiple datasets, no matter whether interventional or observational, biased or unbiased, by remapping it into the former one via graphical transformations. Systematic numerical experiments and a case study on palliative care show the effectiveness of our approach, while hinting at the benefits of fusing heterogeneous data sources to get informative outcomes in case of partial identifiability.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 9 of its 23 references that are in the map. First posted on arXiv 31 Jul 2023.

Builds on

9 of 23 references.

References · 9

  1. 2013Probabilities of Causation: Bounds and Identificationcited by 90
  2. 2013Counterfactual Probabilities: Computational Methods, Bounds and Applicationscited by 67
  3. 2021Partial Counterfactual Identification from Observational and Experimental Datacited by 64
  4. 2021An Automated Approach to Causal Inference in Discrete Settingscited by 42
  5. 2022Personalized Decision Making -- A Conceptual Introductioncited by 30
  6. 2020Structural Causal Models Are (Solvable by) Credal Networkscited by 22
  7. 2022Causal Inference Using Tractable Circuitscited by 12
  8. 2020Causal Expectation-Maximisationcited by 10
  9. 2022Bounding Counterfactuals under Selection Biascited by 6

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 2; 2025: 3; 2026: 3.

9 papers.

  1. 2023Zero-shot Causal Graph Extrapolation from Text via LLMscited by 15
  2. 2025Integral Imprecise Probability Metricscited by 11
  3. 2026Beyond Prediction-Set Size: Quantifying Conformal Uncertainty through Credal Geometrycited by 4
  4. 2024Identifying Causal Effects Under Functional Dependenciescited by 3
  5. 2025Robust Counterfactual Inference in Markov Decision Processescited by 3
  6. 2024Bayesian Networks for Causal Analysis in Socioecological Systemscited by 1
  7. 2025When Do Credal Sets Stabilize? Fixed-Point Theorems for Credal Set Updatescited by 1
  8. 2026Partial Identification under Causal Orders by Linear Programmingcited by 0
  9. 2026Causal Modelling of Support Interventions for Student Competency Assessmentcited by 0