mlsanityData to 14 Oct 2026

An Automated Approach to Causal Inference in Discrete Settings

arXiv 2109.13471 ↗First posted 28 Sep 2021stat.ME cs.LG stat.COcited by 42

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Abstract (arXiv)

When causal quantities cannot be point identified, researchers often pursue partial identification to quantify the range of possible values. However, the peculiarities of applied research conditions can make this analytically intractable. We present a general and automated approach to causal inference in discrete settings. We show causal questions with discrete data reduce to polynomial programming problems, and we present an algorithm to automatically bound causal effects using efficient dual relaxation and spatial branch-and-bound techniques. The user declares an estimand, states assumptions, and provides data (however incomplete or mismeasured). The algorithm then searches over admissible data-generating processes and outputs the most precise possible range consistent with available information -- i.e., sharp bounds -- including a point-identified solution if one exists. Because this search can be computationally intensive, our procedure reports and continually refines non-sharp ranges that are guaranteed to contain the truth at all times, even when the algorithm is not run to completion. Moreover, it offers an additional guarantee we refer to as ε-sharpness, characterizing the worst-case looseness of the incomplete bounds. Analytically validated simulations show the algorithm accommodates classic obstacles, including confounding, selection, measurement error, noncompliance, and nonresponse.

Key facts. Cited by 42 papers in the map (data through 14 Oct 2026). Builds on 16 of its 63 references that are in the map. First posted on arXiv 28 Sep 2021.

Builds on

16 of 63 references.

References · 16

  1. 2016Variational Inference: A Review for Statisticianscited by 1,472
  2. 2013Counterfactual Probabilities: Computational Methods, Bounds and Applicationscited by 67
  3. 2017Nested Markov Properties for Acyclic Directed Mixed Graphscited by 39
  4. 2013On the Testability of Causal Models with Latent and Instrumental Variablescited by 26
  5. 2015Margins of discrete Bayesian networkscited by 26
  6. 2021Bounds on Causal Effects and Application to High Dimensional Datacited by 22
  7. 2020A General Method for Deriving Tight Symbolic Bounds on Causal Effectscited by 18
  8. 2016The Inflation Technique for Causal Inference with Latent Variablescited by 11
  9. 2020Partial Identifiability in Discrete Data With Measurement Errorcited by 10
  10. 2013Instrumentality Tests Revisitedcited by 8
  11. 2013Quantifier Elimination for Statistical Problemscited by 8
  12. 2015Smooth, identifiable supermodels of discrete DAG models with latent variablescited by 8
4 more
  1. 2021The HulC: Confidence Regions from Convex Hullscited by 6
  2. 2017Survivor-complier effects in the presence of selection on treatment, with application to a study of prompt ICU admissioncited by 3
  3. 2020Optimal Confidence Regions for the Multinomial Parametercited by 3
  4. 2020Causal bounds for outcome-dependent sampling in observational studiescited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 9; 2023: 8; 2024: 9; 2025: 5; 2026: 11.

42 papers.

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  1. 2022Stochastic Causal Programming for Bounding Treatment Effectscited by 25
  2. 2023Sharp Bounds for Generalized Causal Sensitivity Analysiscited by 24
  3. 2022Data-Driven Causal Effect Estimation Based on Graphical Causal Modelling: A Surveycited by 19
  4. 2022Partial Identification of Treatment Effects with Implicit Generative Modelscited by 17
  5. 2023A Neural Framework for Generalized Causal Sensitivity Analysiscited by 17
  6. 2022Partial Identification with Noisy Covariates: A Robust Optimization Approachcited by 11
  7. 2024Meta-Learners for Partially-Identified Treatment Effects Across Multiple Environmentscited by 11
  8. 2022Falsification before Extrapolation in Causal Effect Estimationcited by 10
  9. 2024IGC-Net for conditional average potential outcome estimation over timecited by 10
  10. 2023Approximating Counterfactual Bounds while Fusing Observational, Biased and Randomised Data Sourcescited by 9
  11. 2023Efficient Computation of Counterfactual Boundscited by 8
  12. 2024The Fragility of Fairness: Causal Sensitivity Analysis for Fair Machine Learningcited by 8
30 more
  1. 2022Causal Discovery in Linear Latent Variable Models Subject to Measurement Errorcited by 7
  2. 2022On the Complexity of Counterfactual Reasoningcited by 7
  3. 2024Constructing Confidence Intervals for Average Treatment Effects from Multiple Datasetscited by 6
  4. 2023Scalable Computation of Causal Boundscited by 5
  5. 2024Consistency of Neural Causal Partial Identificationcited by 5
  6. 2024Learning Representations of Instruments for Partial Identification of Treatment Effectscited by 4
  7. 2022The Causal Marginal Polytope for Bounding Treatment Effectscited by 3
  8. 2023Bounding probabilities of causation through the causal marginal problemcited by 3
  9. 2025Robust Counterfactual Inference in Markov Decision Processescited by 3
  10. 2026IV-ICL: Bounding Causal Effects with Instrumental Variables via In-Context Learningcited by 3
  11. 2023Tractable Bounding of Counterfactual Queries by Knowledge Compilationcited by 2
  12. 2025Multilinear and Linear Programs for Partially Identifiable Queries in Quasi-Markovian Structural Causal Modelscited by 2
  13. 2026Foundation Models for Partial Causal Identificationcited by 2
  14. 2023Tightening Bounds on Probabilities of Causation By Merging Datasetscited by 1
  15. 2025Your Assumed DAG is Wrong and Here's How To Deal With Itcited by 1
  16. 2025Assessing the robustness of heterogeneous treatment effects in survival analysis under informative censoringcited by 1
  17. 2026Bounds and Identification of Joint Probabilities of Potential Outcomes and Observed Variables under Monotonicity Assumptionscited by 1
  18. 2022Learning to Bound Counterfactual Inference from Observational, Biased and Randomised Datacited by 0
  19. 2024Bounding Causal Effects with Leaky Instrumentscited by 0
  20. 2024A Counterfactual Analysis of the Dishonest Casinocited by 0
  21. 2024Zero Inflation as a Missing Data Problem: a Proxy-based Approachcited by 0
  22. 2025Response to Discussions of "Causal and Counterfactual Views of Missing Data Models"cited by 0
  23. 2026Uncertainty-aware Causal Decision Making via Effect Bound Decompositioncited by 0
  24. 2026Optimal Experiments for Partial Causal Effect Identificationcited by 0
  25. 2026Causal Variational Deep Embedding: A Family of Interventional Generators for Confounded Imagescited by 0
  26. 2026Identification and Bounding of Central Moments of Causal Effects Using Marginal Moments Informationcited by 0
  27. 2026Partial Identification under Causal Orders by Linear Programmingcited by 0
  28. 2026Same Predictions, Different Harms: Causal Auditing of Patient World Modelscited by 0
  29. 2026agent-risk: Risk Assessment for Changes to AI Agentscited by 0
  30. 2026Robust Counterfactuals for Markov Decision Processes under Statistical and Causal Uncertaintiescited by 0