Among them, over-sampling and data augmentation aim to balance the data distribution by oversampling or generating closely related minority classes.

As a result, a naïve ERM learning process will be biased towards the majority classes, making it difficult to generalize to the minority classes.

Class imbalance significantly degrades classification performance, yet its effects are rarely analyzed from a unified theoretical perspective. We propose a principled framework based on three fundamental scales: the imbalance coefficient $η$, the sample--dimension ratio $κ$, and the intrinsic separability $Δ$. Starting from the Gaussian Bayes classifier, we derive closed-form Bayes errors and show how imbalance shifts the discriminant boundary, yielding a deterioration slope that predicts four regimes: Normal, Mild, Extreme, and Catastrophic. Using a balanced high-dimensional genomic dataset, we vary only $η$ while keeping $κ$ and $Δ$ fixed. Across parametric and non-parametric models, empirical degradation closely follows theoretical predictions: minority Recall collapses once $\log(η)$ exceeds $Δ\sqrtκ$, Precision increases asymmetrically, and F1-score and PR-AUC decline in line with the predicted regimes. These results show that the triplet $(η,κ,Δ)$ provides a model-agnostic, geometrically grounded explanation of imbalance-induced deterioration.

Real-world data usually confronts severe class-imbalance problems, where several majority classes have a significantly larger presence in the training set than minority classes. One effective solution is using mixup-based methods to generate synthetic samples to enhance the presence of minority classes. Previous approaches mix the background images from the majority classes and foreground images from theminority classes in a random manner, which ignores the sample-level semantic similarity, possibly resulting in less reasonable or less useful images. In this work, we propose an adaptive image-mixing method based on optimal transport (OT) to incorporate both class-level and sample-level information, which is able to generate semantically reasonable and meaningful mixed images for minority classes. Due toits flexibility, our method can be combined with existing long-tailed classification methods to enhance their performance and it can also serve as a general data augmentation method for balanced datasets. Extensive experiments indicate that our method achieves effective performance for long-tailed classification tasks.

Real-world datasets are typically imbalanced in the sense that only a few classes have numerous samples, while many classes are associated with only a few samples. As a result, a naive ERM learning process will be biased towards the majority classes, making it difficult to generalize to the minority classes. To address this issue, one simple but effective approach is to modify the loss function to emphasize the learning on minority classes, such as re-weighting the losses or adjusting the logits via class-dependent terms. However, existing generalization analysis of such losses is still coarse-grained and fragmented, failing to explain some empirical results. To bridge this gap between theory and practice, we propose a novel technique named data-dependent contraction to capture how these modified losses handle different classes. On top of this technique, a fine-grained generalization bound is established for imbalanced learning, which helps reveal the mystery of re-weighting and logit-adjustment in a unified manner. Furthermore, a principled learning algorithm is developed based on the theoretical insights. Finally, the empirical results on benchmark datasets not only validate the theoretical results but also demonstrate the effectiveness of the proposed method.