mlsanityData to 7 Oct 2026

Causal Inference Through the Structural Causal Marginal Problem

arXiv 2202.01300 ↗First posted 2 Feb 2022cs.AI cs.LGcited by 22

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Abstract (arXiv)

We introduce an approach to counterfactual inference based on merging information from multiple datasets. We consider a causal reformulation of the statistical marginal problem: given a collection of marginal structural causal models (SCMs) over distinct but overlapping sets of variables, determine the set of joint SCMs that are counterfactually consistent with the marginal ones. We formalise this approach for categorical SCMs using the response function formulation and show that it reduces the space of allowed marginal and joint SCMs. Our work thus highlights a new mode of falsifiability through additional variables, in contrast to the statistical one via additional data.

Key facts. Cited by 22 papers in the map (data through 7 Oct 2026). Builds on 17 of its 66 references that are in the map. First posted on arXiv 2 Feb 2022.

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17 of 66 references.

References · 17

  1. 2019Advances and Open Problems in Federated Learningcited by 3,021
  2. 2021Convex optimizationcited by 2,479
  3. 2013Direct and Indirect Effectscited by 276
  4. 2016Foundations of Structural Causal Models with Cycles and Latent Variablescited by 134
  5. 2017Causal Consistency of Structural Equation Modelscited by 114
  6. 2018Abstracting Causal Modelscited by 104
  7. 2013Probabilities of Causation: Bounds and Identificationcited by 89
  8. 2015External Validity: From Do-Calculus to Transportability Across Populationscited by 75
  9. 2013Counterfactual Probabilities: Computational Methods, Bounds and Applicationscited by 67
  10. 2021Partial Counterfactual Identification from Observational and Experimental Datacited by 64
  11. 2019Approximate Causal Abstractioncited by 62
  12. 2014Constraint-based Causal Discovery from Multiple Interventions over Overlapping Variable Setscited by 48
5 more
  1. 2021Nested Counterfactual Identification from Arbitrary Surrogate Experimentscited by 38
  2. 2015Multi-Level Cause-Effect Systemscited by 30
  3. 2020A Class of Algorithms for General Instrumental Variable Modelscited by 28
  4. 2021BayesIMP: Uncertainty Quantification for Causal Data Fusioncited by 21
  5. 2021Obtaining Causal Information by Merging Datasets with MAXENTcited by 9

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 11; 2024: 4; 2025: 3; 2026: 3.

22 papers.

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  1. 2023Multi-View Causal Representation Learning with Partial Observabilitycited by 72
  2. 2023Counterfactual Identifiability of Bijective Causal Modelscited by 42
  3. 2023Self-Compatibility: Evaluating Causal Discovery without Ground Truthcited by 22
  4. 2023Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Modelcited by 14
  5. 2024Identifiable Causal Representation Learning: Unsupervised, Multi-View, and Multi-Environmentcited by 12
  6. 2022Phenomenological Causalitycited by 7
  7. 2024Counterfactual Causal Inference in Natural Language with Large Language Modelscited by 7
  8. 2023A Survey of Methods, Challenges and Perspectives in Causalitycited by 6
  9. 2025Counterfactual Identifiability via Dynamic Optimal Transportcited by 5
  10. 2023Out-of-Variable Generalization for Discriminative Modelscited by 4
  11. 2023Results on Counterfactual Invariancecited by 4
  12. 2026Structural Causal Bottleneck Modelscited by 4
10 more
  1. 2023Bounding probabilities of causation through the causal marginal problemcited by 3
  2. 2023Reinterpreting causal discovery as the task of predicting unobserved joint statisticscited by 3
  3. 2025On Different Notions of Redundancy in Conditional-Independence-Based Discovery of Graphical Modelscited by 3
  4. 2024Estimating Joint Interventional Distributions from Marginal Interventional Datacited by 2
  5. 2024Cross-validating causal discovery via Leave-One-Variable-Outcited by 2
  6. 2023Tightening Bounds on Probabilities of Causation By Merging Datasetscited by 1
  7. 2023Variational Counterfactual Prediction under Runtime Domain Corruptioncited by 0
  8. 2025Learning Joint Interventional Effects from Single-Variable Interventions in Additive Modelscited by 0
  9. 2026Multi-Level Causal Embeddingscited by 0
  10. 2026Operationalising Relative Causal Knowledge: Backbone Identifiability from Private Reports on a Shared Outcomecited by 0