Concentration and excess risk bounds for imbalanced classification with synthetic oversampling

2025-10-23

AI Summary

This paper addresses the lack of theoretical foundations for synthetic oversampling methods such as SMOTE in imbalanced classification. We establish, for the first time, a statistical learning theory framework for such methods. By integrating uniform concentration inequalities with nonparametric estimation, we rigorously characterize the convergence between the empirical risk—computed over synthetically augmented data—and the population risk under the true data distribution, and derive a nonparametric excess risk bound for kernel classifiers. Our key contributions are: (1) the first unified concentration bound applicable to SMOTE-like oversampling schemes; (2) a theoretically grounded criterion for joint tuning of oversampling parameters (e.g., neighborhood size, synthesis ratio) and classifier hyperparameters; and (3) empirical validation demonstrating that the derived bound effectively predicts and guides generalization performance in practice.

Technology Category

• Machine Learning: Learning Theory
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

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

Problem

• Analyzing theoretical foundations of SMOTE for imbalanced classification
• Deriving concentration bounds between synthetic and true minority distributions
• Providing excess risk guarantees for kernel classifiers with synthetic data

Innovation

• Developed theoretical framework for SMOTE analysis
• Derived concentration bound for synthetic data risk
• Provided excess risk guarantee for kernel classifiers