Concentration and excess risk bounds for imbalanced classification with synthetic oversampling
Touqeer Ahmad, Mohammadreza Mousavi Kalan, François Portier, Gilles Stupfler
Oversampling synthetic minority examples using $\textsc{Smote}$ 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 $\textsc{Smote}$ and related methods when classifiers are trained on synthetic data. First, we establish an exponential inequality that characterizes the gap between the empirical risk computed on synthetic samples and the true population risk on the minority class. Second, we show that a kernel-based classification rule trained on synthetic data can achieve the minimax rate of convergence. This leads to practical guidelines for better parameter tuning of both $\textsc{Smote}$ and the downstream learning algorithm. Numerical experiments are provided to illustrate and support the theoretical findings.