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

When dealing with imbalanced classification data, reweighting the loss functionis a standard procedure allowing to equilibrate between the true positive and truenegative rates within the risk measure. Despite significant theoretical work inthis area, existing results do not adequately address a main challenge within theimbalanced classification framework, which is the negligible size of one classin relation to the full sample size and the need to rescale the risk function by aprobability tending to zero. To address this gap, we present two novel contributions in the setting where the rare class probability approaches zero: (1) a non asymptotic fast rate probability bound for constrained balanced empirical risk minimization, and (2) a consistent upper bound for balanced nearest neighbors estimates. Our findings provide a clearer understanding of the benefits of class-weighting in realistic settings, opening new avenues for further research in this field.