A Unified Generalization Analysis of Re-Weighting and Logit-Adjustment for Imbalanced Learning

Due to the inherent imbalance in real-world datasets, naïve Empirical Risk Minimization (ERM) tends to bias the learning process towards the majority classes, hindering generalization to minority classes. To rebalance the learning process, one straightforward yet effective approach is to modify the loss function via class-dependent terms, such as re-weighting and logit-adjustment. However, existing analysis of these loss-oriented methods remains coarse-grained and fragmented, failing to explain some empirical results. After reviewing prior work, we find that the properties used through their analysis are typically global, i.e., defined over the whole dataset. Hence, these properties fail to effectively capture how class-dependent terms influence the learning process. To bridge this gap, we turn to explore the localized versions of such properties i.e., defined within each class. Specifically, we employ localized calibration to provide consistency validation across a broader range of losses and localized Lipschitz continuity to provide a fine-grained generalization bound. In this way, we reach a unified perspective for improving and adjusting loss-oriented methods. Finally, a principled learning algorithm is developed based on these insights. Empirical results on both traditional ResNets and foundation models validate our theoretical analyses and demonstrate the effectiveness of the proposed method.