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Real-world datasets are typically imbalanced in the sense that only a fewclasses have numerous samples, while many classes are associated with only afew samples. As a result, a na\"ive ERM learning process will be biased towardsthe majority classes, making it difficult to generalize to the minorityclasses. To address this issue, one simple but effective approach is to modifythe loss function to emphasize the learning on minority classes, such asre-weighting the losses or adjusting the logits via class-dependent terms.However, existing generalization analysis of such losses is stillcoarse-grained and fragmented, failing to explain some empirical results. Tobridge this gap, we propose a novel technique named data-dependent contractionto capture how these modified losses handle different classes. On top of thistechnique, a fine-grained generalization bound is established for imbalancedlearning, which helps reveal the mystery of re-weighting and logit-adjustmentin a unified manner. Furthermore, a principled learning algorithm is developedbased on the theoretical insights. Finally, the empirical results on benchmarkdatasets not only validate the theoretical results but also demonstrate theeffectiveness of the proposed method.

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