arXiv subjects

Zhengchi Ma

Publications and source records attributed to Zhengchi Ma.

4 recordsLinked to original sources

arXiv2026

When Does Synthetic Data Augmentation Improve Score-Based Imbalanced Classification?

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.

stat.ML↗

arXiv2026

Synthetic Augmentation in Imbalanced Learning: When It Helps, When It Hurts, and How Much to Add

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.

stat.ML↗

arXiv2025

Bias-Corrected Data Synthesis for Imbalanced Learning

Imbalanced data, where the positive samples represent only a small proportion compared to the negative samples, makes it challenging for classification problems to balance the false positive and false negative rates. A common approach to addressing the challenge involves generating synthetic data for the minority group and then training classification models with both observed and synthetic data. However, since the synthetic data depends on the observed data and fails to replicate the original data distribution accurately, prediction accuracy is reduced when the synthetic data is na\"{i}vely treated as the true data. In this paper, we address the bias introduced by synthetic data and provide consistent estimators for this bias by borrowing information from the majority group. We propose a bias correction procedure to mitigate the adverse effects of synthetic data, enhancing prediction accuracy while avoiding overfitting. This procedure is extended to broader scenarios with imbalanced data, such as imbalanced multi-task learning and causal inference. Theoretical properties, including bounds on bias estimation errors and improvements in prediction accuracy, are provided. Simulation results and data analysis on handwritten digit datasets demonstrate the effectiveness of our method.

stat.ML↗

arXiv2024

Optimal Estimation of Shared Singular Subspaces across Multiple Noisy Matrices

Estimating singular subspaces from noisy matrices is a fundamental problem with wide-ranging applications across various fields. Driven by the challenges of data integration and multi-view analysis, this study focuses on estimating shared singular subspaces across multiple matrices within a low-rank matrix denoising framework. A common approach for this task is to perform singular value decomposition on the stacked matrix (Stack-SVD), which concatenates all the matrices. We establish that Stack-SVD achieves minimax rate-optimality when the true singular subspaces of the noisy matrices are identical, whereas a popular alternative approach based on SVD of concatenated singular vector matrices (Average-SVD) can be sub-optimal. We then tackle the more complex scenario where the true singular subspaces are only partially shared across matrices. For various cases of partial sharing, we rigorously characterize the conditions under which Stack-SVD remains effective, achieves minimax optimality, or fails to deliver consistent estimates, offering theoretical insights into its practical applicability. To address the limitations of Stack-SVD in scenarios with partial sharing, we propose novel estimators and an efficient algorithm designed to identify both shared and unshared singular vectors. We further prove that these methods attain minimax rate-optimality under partial sharing. Extensive simulations and real-world data applications demonstrate the advantages of our proposed approach.

math.ST↗