mlsanityData to 7 Oct 2026

Causal inference using invariant prediction: identification and confidence intervals

arXiv 1501.01332 ↗First posted 6 Jan 2015stat.ME cs.LGcited by 533

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Abstract (arXiv)

What is the difference of a prediction that is made with a causal model and a non-causal model? Suppose we intervene on the predictor variables or change the whole environment. The predictions from a causal model will in general work as well under interventions as for observational data. In contrast, predictions from a non-causal model can potentially be very wrong if we actively intervene on variables. Here, we propose to exploit this invariance of a prediction under a causal model for causal inference: given different experimental settings (for example various interventions) we collect all models that do show invariance in their predictive accuracy across settings and interventions. The causal model will be a member of this set of models with high probability. This approach yields valid confidence intervals for the causal relationships in quite general scenarios. We examine the example of structural equation models in more detail and provide sufficient assumptions under which the set of causal predictors becomes identifiable. We further investigate robustness properties of our approach under model misspecification and discuss possible extensions. The empirical properties are studied for various data sets, including large-scale gene perturbation experiments.

Key facts. Cited by 533 papers in the map (data through 7 Oct 2026). First posted on arXiv 6 Jan 2015.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 70; 2022: 114; 2023: 96; 2024: 79; 2025: 73; 2026: 101.

533 papers.

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  1. 2021Towards Out-Of-Distribution Generalization: A Surveycited by 431
  2. 2022Last Layer Re-Training is Sufficient for Robustness to Spurious Correlationscited by 379
  3. 2021Invariance Principle Meets Information Bottleneck for Out-of-Distribution Generalizationcited by 220
  4. 2021Towards Causal Representation Learningcited by 207
  5. 2022Surgical Fine-Tuning Improves Adaptation to Distribution Shiftscited by 205
  6. 2021Fishr: Invariant Gradient Variances for Out-of-Distribution Generalizationcited by 186
  7. 2021Causal Inference in Natural Language Processing: Estimation, Prediction, Interpretation and Beyondcited by 177
  8. 2022Handling Distribution Shifts on Graphs: An Invariance Perspectivecited by 163
  9. 2022Diverse Weight Averaging for Out-of-Distribution Generalizationcited by 148
  10. 2022Learning Causally Invariant Representations for Out-of-Distribution Generalization on Graphscited by 144
  11. 2022GOOD: A Graph Out-of-Distribution Benchmarkcited by 140
  12. 2022Causality Inspired Representation Learning for Domain Generalizationcited by 136
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  1. 2021On Calibration and Out-of-domain Generalizationcited by 134
  2. 2021Does Invariant Risk Minimization Capture Invariance?cited by 116
  3. 2023Nonparametric Identifiability of Causal Representations from Unknown Interventionscited by 105
  4. 2021Independent mechanism analysis, a new concept?cited by 96
  5. 2021Towards a Theoretical Framework of Out-of-Distribution Generalizationcited by 94
  6. 2023Learning Linear Causal Representations from Interventions under General Nonlinear Mixingcited by 92
  7. 2021Towards Principled Disentanglement for Domain Generalizationcited by 91
  8. 2021Evading the Simplicity Bias: Training a Diverse Set of Models Discovers Solutions with Superior OOD Generalizationcited by 83
  9. 2021Efficient Neural Causal Discovery without Acyclicity Constraintscited by 82
  10. 2021Counterfactual Invariance to Spurious Correlations: Why and How to Pass Stress Testscited by 77
  11. 2021Can Subnetwork Structure be the Key to Out-of-Distribution Generalization?cited by 75
  12. 2022Domain-Adjusted Regression or: ERM May Already Learn Features Sufficient for Out-of-Distribution Generalizationcited by 69
  13. 2021On the Impact of Spurious Correlation for Out-of-distribution Detectioncited by 68
  14. 2022Learning to Induce Causal Structurecited by 68
  15. 2022Causal Machine Learning for Healthcare and Precision Medicinecited by 68
  16. 2022Probable Domain Generalization via Quantile Risk Minimizationcited by 66
  17. 2021Visual Representation Learning Does Not Generalize Strongly Within the Same Domaincited by 60
  18. 2022ZIN: When and How to Learn Invariance Without Environment Partition?cited by 58
  19. 2022Transferability in Deep Learning: A Surveycited by 57
  20. 2022Causal Discovery in Heterogeneous Environments Under the Sparse Mechanism Shift Hypothesiscited by 54
  21. 2021Systematic Evaluation of Causal Discovery in Visual Model Based Reinforcement Learningcited by 53
  22. 2022Bayesian Prompt Learning for Image-Language Model Generalizationcited by 51
  23. 2021Source-Free Adaptation to Measurement Shift via Bottom-Up Feature Restorationcited by 50
  24. 2022Interventions, Where and How? Experimental Design for Causal Models at Scalecited by 49
  25. 2022Out-of-distribution Generalization with Causal Invariant Transformationscited by 45
  26. 2023MuggleMath: Assessing the Impact of Query and Response Augmentation on Math Reasoningcited by 45
  27. 2021Variational Causal Networks: Approximate Bayesian Inference over Causal Structurescited by 43
  28. 2023Model Agnostic Sample Reweighting for Out-of-Distribution Learningcited by 43
  29. 2023Causal Discovery from Temporal Data: An Overview and New Perspectivescited by 43
  30. 2021Nonlinear Invariant Risk Minimization: A Causal Approachcited by 42
  31. 2022Causal de Finetti: On the Identification of Invariant Causal Structure in Exchangeable Datacited by 42
  32. 2023Does Invariant Graph Learning via Environment Augmentation Learn Invariance?cited by 42
  33. 2023Spawrious: A Benchmark for Fine Control of Spurious Correlation Biasescited by 41
  34. 2021Learning Neural Causal Models with Active Interventionscited by 40
  35. 2021Towards Robust and Adaptive Motion Forecasting: A Causal Representation Perspectivecited by 40
  36. 2022From Statistical to Causal Learningcited by 40
  37. 2022Pareto Invariant Risk Minimization: Towards Mitigating the Optimization Dilemma in Out-of-Distribution Generalizationcited by 38
  38. 2022Invariant and Transportable Representations for Anti-Causal Domain Shiftscited by 37

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