Zhengchi Ma

Zhengchi Ma, Pengfei Lyu, Anru R. Zhang

Synthetic data augmentation is widely used to mitigate class imbalance, but its theoretical effects on score-based classification remain poorly understood. This paper develops a framework for characterizing when synthetic minority augmentation can improve threshold-integrated and threshold-optimized metrics, including AUROC, AUPRC, best-threshold balanced accuracy, and best-threshold \(\F_1\) score. We separate the effect of augmentation into two components: a change in effective class weighting and a discrepancy between the synthetic and true minority distributions. Under well-specified score models, the raw estimator already targets the likelihood-ratio ordering, which is population-optimal for the metrics considered. Consequently, augmentation cannot provide a fundamental population-level improvement beyond possible finite-sample variance reduction, and may introduce additional bias through synthetic distributional error. We further establish minimax lower bounds showing that the raw estimator already achieves the optimal metric-regret rate in the well-specified regime. Under misspecification, however, augmentation can play a qualitatively different role: by changing the effective class balance, it can alter the restricted-class projection and correct ranking errors induced by the raw imbalanced objective. We provide explicit improvement bounds quantifying the roles of approximation error, finite-sample estimation error, and synthetic distributional error. Simulation studies corroborate the theory, demonstrating limited gains under well-specification and nontrivial but nonmonotone improvements under misspecification.

Zhengchi Ma, Anru R. Zhang

Imbalanced classification often causes standard training procedures to prioritize the majority class and perform poorly on rare but important cases. A classic and widely used remedy is to augment the minority class with synthetic samples, but two basic questions remain under-resolved: when does synthetic augmentation actually help, and how many synthetic samples should be generated? We develop a unified statistical framework for synthetic augmentation in imbalanced learning, studying models trained on imbalanced data augmented with synthetic minority samples. Our theory shows that synthetic data is not always beneficial. In a "local symmetry" regime, imbalance is not the dominant source of error, so adding synthetic samples cannot improve learning rates and can even degrade performance by amplifying generator mismatch. When augmentation can help ("local asymmetry"), the optimal synthetic size depends on generator accuracy and on whether the generator's residual mismatch is directionally aligned with the intrinsic majority-minority shift. This structure can make the best synthetic size deviate from naive full balancing. Practically, we recommend Validation-Tuned Synthetic Size (VTSS): select the synthetic size by minimizing balanced validation loss over a range centered near the fully balanced baseline, while allowing meaningful departures. Extensive simulations and real data analysis further support our findings.