Towards Understanding Variants of Invariant Risk Minimization through the Lens of Calibration

Machine learning models traditionally assume that training and test data are independently and identically distributed. However, in real-world applications, the test distribution often differs from training. This problem, known as out-of-distribution generalization, challenges conventional models. Invariant Risk Minimization (IRM) emerges as a solution, aiming to identify features invariant across different environments to enhance out-of-distribution robustness. However, IRM's complexity, particularly its bi-level optimization, has led to the development of various approximate methods. Our study investigates these approximate IRM techniques, employing the Expected Calibration Error (ECE) as a key metric. ECE, which measures the reliability of model prediction, serves as an indicator of whether models effectively capture environment-invariant features. Through a comparative analysis of datasets with distributional shifts, we observe that Information Bottleneck-based IRM, which condenses representational information, achieves a balance in improving ECE while preserving accuracy relatively. This finding is pivotal, as it demonstrates a feasible path to maintaining robustness without compromising accuracy. Nonetheless, our experiments also caution against over-regularization, which can diminish accuracy. This underscores the necessity for a systematic approach in evaluating out-of-distribution generalization metrics, one that beyond mere accuracy to address the nuanced interplay between accuracy and calibration.