Theoretical Convergence of SMOTE-Generated Samples

February 09, 2026

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📝 Original Info

Title: Theoretical Convergence of SMOTE-Generated Samples
ArXiv ID: 2601.01927
Date: 2026-01-05
Authors: Firuz Kamalov, Hana Sulieman, Witold Pedrycz

📝 Abstract

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 reallife and synthetic data. Our work provides a foundational understanding that enhances data augmentation techniques beyond imbalanced data scenarios.

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Theoretical Convergence of SMOTE-Generated Samples

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