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When dealing with imbalanced classification data, reweighting the lossfunction is a standard procedure allowing to equilibrate between the truepositive and true negative rates within the risk measure. Despite significanttheoretical work in this area, existing results do not adequately address amain challenge within the imbalanced classification framework, which is thenegligible size of one class in relation to the full sample size and the needto rescale the risk function by a probability tending to zero. To address thisgap, we present two novel contributions in the setting where the rare classprobability approaches zero: (1) a non asymptotic fast rate probability boundfor constrained balanced empirical risk minimization, and (2) a consistentupper bound for balanced nearest neighbors estimates. Our findings provide aclearer understanding of the benefits of class-weighting in realistic settings,opening new avenues for further research in this field.

Sharp error bounds for imbalanced classification: how many examples in the minority class?