Sharp error bounds for imbalanced classification: how many examples in the minority class?
This addresses a theoretical gap in imbalanced classification for machine learning practitioners dealing with rare classes, though it appears incremental on existing reweighting methods.
The paper tackles the challenge of imbalanced classification where one class probability approaches zero, providing non-asymptotic fast rate probability bounds for constrained balanced empirical risk minimization and consistent upper bounds for balanced nearest neighbors estimates.
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.