# Causal inference using invariant prediction: identification and confidence intervals

arXiv: https://arxiv.org/abs/1501.01332 · HTML: https://mlsanity.com/paper/1501.01332/

## Key facts

- Cited by 536 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jan 2015.

## Built on by (most cited first, 30 of 536)

- [Towards Out-Of-Distribution Generalization: A Survey](https://mlsanity.com/paper/2108.13624/) (2021)
- [Last Layer Re-Training is Sufficient for Robustness to Spurious Correlations](https://mlsanity.com/paper/2204.02937/) (2022)
- [Invariance Principle Meets Information Bottleneck for Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.06607/) (2021)
- [Towards Causal Representation Learning](https://mlsanity.com/paper/2102.11107/) (2021)
- [Surgical Fine-Tuning Improves Adaptation to Distribution Shifts](https://mlsanity.com/paper/2210.11466/) (2022)
- [Fishr: Invariant Gradient Variances for Out-of-Distribution Generalization](https://mlsanity.com/paper/2109.02934/) (2021)
- [Causal Inference in Natural Language Processing: Estimation, Prediction, Interpretation and Beyond](https://mlsanity.com/paper/2109.00725/) (2021)
- [Handling Distribution Shifts on Graphs: An Invariance Perspective](https://mlsanity.com/paper/2202.02466/) (2022)
- [Diverse Weight Averaging for Out-of-Distribution Generalization](https://mlsanity.com/paper/2205.09739/) (2022)
- [Learning Causally Invariant Representations for Out-of-Distribution Generalization on Graphs](https://mlsanity.com/paper/2202.05441/) (2022)
- [GOOD: A Graph Out-of-Distribution Benchmark](https://mlsanity.com/paper/2206.08452/) (2022)
- [Causality Inspired Representation Learning for Domain Generalization](https://mlsanity.com/paper/2203.14237/) (2022)
- [On Calibration and Out-of-domain Generalization](https://mlsanity.com/paper/2102.10395/) (2021)
- [Does Invariant Risk Minimization Capture Invariance?](https://mlsanity.com/paper/2101.01134/) (2021)
- [Nonparametric Identifiability of Causal Representations from Unknown Interventions](https://mlsanity.com/paper/2306.00542/) (2023)
- [Independent mechanism analysis, a new concept?](https://mlsanity.com/paper/2106.05200/) (2021)
- [Towards a Theoretical Framework of Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.04496/) (2021)
- [Learning Linear Causal Representations from Interventions under General Nonlinear Mixing](https://mlsanity.com/paper/2306.02235/) (2023)
- [Towards Principled Disentanglement for Domain Generalization](https://mlsanity.com/paper/2111.13839/) (2021)
- [Evading the Simplicity Bias: Training a Diverse Set of Models Discovers Solutions with Superior OOD Generalization](https://mlsanity.com/paper/2105.05612/) (2021)
- [Efficient Neural Causal Discovery without Acyclicity Constraints](https://mlsanity.com/paper/2107.10483/) (2021)
- [Counterfactual Invariance to Spurious Correlations: Why and How to Pass Stress Tests](https://mlsanity.com/paper/2106.00545/) (2021)
- [Can Subnetwork Structure be the Key to Out-of-Distribution Generalization?](https://mlsanity.com/paper/2106.02890/) (2021)
- [Domain-Adjusted Regression or: ERM May Already Learn Features Sufficient for Out-of-Distribution Generalization](https://mlsanity.com/paper/2202.06856/) (2022)
- [On the Impact of Spurious Correlation for Out-of-distribution Detection](https://mlsanity.com/paper/2109.05642/) (2021)
- [Learning to Induce Causal Structure](https://mlsanity.com/paper/2204.04875/) (2022)
- [Causal Machine Learning for Healthcare and Precision Medicine](https://mlsanity.com/paper/2205.11402/) (2022)
- [Probable Domain Generalization via Quantile Risk Minimization](https://mlsanity.com/paper/2207.09944/) (2022)
- [Visual Representation Learning Does Not Generalize Strongly Within the Same Domain](https://mlsanity.com/paper/2107.08221/) (2021)
- [ZIN: When and How to Learn Invariance Without Environment Partition?](https://mlsanity.com/paper/2203.05818/) (2022)

## 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.