# Conformal Inference for Invariant Risk Minimization

arXiv: https://arxiv.org/abs/2305.12686 · HTML: https://mlsanity.com/paper/2305.12686/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 34 references that are in the map.
- First posted on arXiv 22 May 2023.

## Builds on (most cited first, 23 of 23)

- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Measuring Robustness to Natural Distribution Shifts in Image Classification](https://mlsanity.com/paper/2007.00644/) (2020)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Environment Inference for Invariant Learning](https://mlsanity.com/paper/2010.07249/) (2020)
- [The Risks of Invariant Risk Minimization](https://mlsanity.com/paper/2010.05761/) (2020)
- [Domain Generalization using Causal Matching](https://mlsanity.com/paper/2006.07500/) (2020)
- [Invariance Principle Meets Information Bottleneck for Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.06607/) (2021)
- [Invariant Risk Minimization Games](https://mlsanity.com/paper/2002.04692/) (2020)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Invariant Rationalization](https://mlsanity.com/paper/2003.09772/) (2020)
- [Conformal Prediction: a Unified Review of Theory and New Challenges](https://mlsanity.com/paper/2005.07972/) (2020)
- [Localized Conformal Prediction: A Generalized Inference Framework for Conformal Prediction](https://mlsanity.com/paper/2106.08460/) (2021)
- [Invariant Information Bottleneck for Domain Generalization](https://mlsanity.com/paper/2106.06333/) (2021)
- [Robust Validation: Confident Predictions Even When Distributions Shift](https://mlsanity.com/paper/2008.04267/) (2020)
- [Adaptive, Distribution-Free Prediction Intervals for Deep Networks](https://mlsanity.com/paper/1905.10634/) (2019)
- [Distribution-Free Prediction Sets for Two-Layer Hierarchical Models](https://mlsanity.com/paper/1809.07441/) (2018)
- [Provable Domain Generalization via Invariant-Feature Subspace Recovery](https://mlsanity.com/paper/2201.12919/) (2022)
- [A moment-matching Ferguson and Klass algorithm](https://mlsanity.com/paper/1606.02566/) (2016)

## Abstract (arXiv)

The application of machine learning models can be significantly impeded by the occurrence of distributional shifts, as the assumption of homogeneity between the population of training and testing samples in machine learning and statistics may not be feasible in practical situations. One way to tackle this problem is to use invariant learning, such as invariant risk minimization (IRM), to acquire an invariant representation that aids in generalization with distributional shifts. This paper develops methods for obtaining distribution-free prediction regions to describe uncertainty estimates for invariant representations, accounting for the distribution shifts of data from different environments. Our approach involves a weighted conformity score that adapts to the specific environment in which the test sample is situated. We construct an adaptive conformal interval using the weighted conformity score and prove its conditional average under certain conditions. To demonstrate the effectiveness of our approach, we conduct several numerical experiments, including simulation studies and a practical example using real-world data.