Concentration and excess risk bounds for imbalanced classification with synthetic oversampling
This work addresses a theoretical gap for practitioners using SMOTE in imbalanced classification, though it is incremental as it builds on existing methods.
The paper tackles the lack of theoretical foundations for synthetic oversampling methods like SMOTE in imbalanced classification by deriving a uniform concentration bound and a nonparametric excess risk guarantee for kernel-based classifiers trained on synthetic data, leading to practical tuning guidelines supported by numerical experiments.
Synthetic oversampling of minority examples using SMOTE and its variants is a leading strategy for addressing imbalanced classification problems. Despite the success of this approach in practice, its theoretical foundations remain underexplored. We develop a theoretical framework to analyze the behavior of SMOTE and related methods when classifiers are trained on synthetic data. We first derive a uniform concentration bound on the discrepancy between the empirical risk over synthetic minority samples and the population risk on the true minority distribution. We then provide a nonparametric excess risk guarantee for kernel-based classifiers trained using such synthetic data. These results lead to practical guidelines for better parameter tuning of both SMOTE and the downstream learning algorithm. Numerical experiments are provided to illustrate and support the theoretical findings