  When dealing with imbalanced classification data, reweighting the loss
function is a standard procedure allowing to equilibrate between the true
positive and true negative rates within the risk measure. Despite significant
theoretical work in this area, existing results do not adequately address a
main challenge within the imbalanced classification framework, which is the
negligible size of one class in relation to the full sample size and the need
to rescale the risk function by a probability 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.
