Conformal Inference for Invariant Risk Minimization
This work addresses uncertainty estimation for invariant learning methods, which is crucial for improving generalization in practical applications with distribution shifts, though it appears incremental by extending conformal inference to IRM.
The paper tackles the problem of distributional shifts in machine learning by developing distribution-free prediction regions for invariant representations, using a weighted conformity score that adapts to specific environments and proving conditional average coverage under certain conditions.
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.