Theoretical Convergence of SMOTE-Generated Samples
This provides a foundational theoretical understanding for practitioners using SMOTE in applications like healthcare and network security, though it is incremental as it builds on existing empirical work.
The paper tackled the problem of validating SMOTE's theoretical convergence properties for imbalanced data, proving that synthetic samples converge in probability and in mean to the underlying distribution, with faster convergence for lower nearest neighbor ranks.
Imbalanced data affects a wide range of machine learning applications, from healthcare to network security. As SMOTE is one of the most popular approaches to addressing this issue, it is imperative to validate it not only empirically but also theoretically. In this paper, we provide a rigorous theoretical analysis of SMOTE's convergence properties. Concretely, we prove that the synthetic random variable Z converges in probability to the underlying random variable X. We further prove a stronger convergence in mean when X is compact. Finally, we show that lower values of the nearest neighbor rank lead to faster convergence offering actionable guidance to practitioners. The theoretical results are supported by numerical experiments using both real-life and synthetic data. Our work provides a foundational understanding that enhances data augmentation techniques beyond imbalanced data scenarios.