  Class imbalance in real-world data poses a common bottleneck for machine
learning tasks, since achieving good generalization on under-represented
examples is often challenging. Mitigation strategies, such as under or
oversampling the data depending on their abundances, are routinely proposed and
tested empirically, but how they should adapt to the data statistics remains
poorly understood. In this work, we determine exact analytical expressions of
the generalization curves in the high-dimensional regime for linear classifiers
(Support Vector Machines). We also provide a sharp prediction of the effects of
under/oversampling strategies depending on class imbalance, first and second
moments of the data, and the metrics of performance considered. We show that
mixed strategies involving under and oversampling of data lead to performance
improvement. Through numerical experiments, we show the relevance of our
theoretical predictions on real datasets, on deeper architectures and with
sampling strategies based on unsupervised probabilistic models.
