Theoretical Convergence of SMOTE-Generated Samples

• URL: http://arxiv.org/abs/2601.01927v1
• Date: Mon, 05 Jan 2026 09:19:45 GMT
• Title: Theoretical Convergence of SMOTE-Generated Samples
• Authors: Firuz Kamalov, Hana Sulieman, Witold Pedrycz,
• Abstract summary: We provide a rigorous theoretical analysis of SMOTE's convergence properties.<n>We prove that the synthetic random variable Z converges in probability to the underlying random variable X.<n>Lower values of the nearest neighbor rank lead to faster convergence.
• Score: 47.26889442476884
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 real-life and synthetic data. Our work provides a foundational understanding that enhances data augmentation techniques beyond imbalanced data scenarios.

Related papers

• Sharp Convergence Rates for Masked Diffusion Models [53.117058231393834]
  We develop a total-variation based analysis for the Euler method that overcomes limitations.<n>Our results relax assumptions on score estimation, improve parameter dependencies, and establish convergence guarantees.<n>Overall, our analysis introduces a direct TV-based error decomposition along the CTMC trajectory and a decoupling-based path-wise analysis for FHS.
  arXiv  Detail & Related papers  (2026-02-26T00:47:51Z)
• Beyond Real Data: Synthetic Data through the Lens of Regularization [9.459299281438074]
  Synthetic data can improve generalization when real data is scarce, but excessive reliance may introduce distributional mismatches that degrade performance.<n>We present a learning-theoretic framework to quantify the trade-off between synthetic and real data.
  arXiv  Detail & Related papers  (2025-10-09T11:33:09Z)
• A Sample Efficient Conditional Independence Test in the Presence of Discretization [54.047334792855345]
  Conditional Independence (CI) tests directly to discretized data can lead to incorrect conclusions.<n>Recent advancements have sought to infer the correct CI relationship between the latent variables through binarizing observed data.<n>Motivated by this, this paper introduces a sample-efficient CI test that does not rely on the binarization process.
  arXiv  Detail & Related papers  (2025-06-10T12:41:26Z)
• A Scalable Nyström-Based Kernel Two-Sample Test with Permutations [9.849635250118912]
  Two-sample hypothesis testing is a fundamental problem in statistics and machine learning.<n>In this work, we use a Nystr"om approximation of the maximum mean discrepancy (MMD) to design a computationally efficient and practical testing algorithm.
  arXiv  Detail & Related papers  (2025-02-19T09:22:48Z)
• Do we need rebalancing strategies? A theoretical and empirical study around SMOTE and its variants [5.561618915244982]
  We derive several non-asymptotic upper bound on SMOTE density.<n>We prove that SMOTE tends to copy the original minority samplesally.<n>We adapt SMOTE based on our theoretical findings to introduce two new variants.
  arXiv  Detail & Related papers  (2024-02-06T09:07:41Z)
• TIC-TAC: A Framework for Improved Covariance Estimation in Deep Heteroscedastic Regression [109.69084997173196]
  Deepscedastic regression involves jointly optimizing the mean and covariance of the predicted distribution using the negative log-likelihood. Recent works show that this may result in sub-optimal convergence due to the challenges associated with covariance estimation. We study two questions: (1) Does the predicted covariance truly capture the randomness of the predicted mean? Our results show that not only does TIC accurately learn the covariance, it additionally facilitates an improved convergence of the negative log-likelihood.
  arXiv  Detail & Related papers  (2023-10-29T09:54:03Z)
• Prototype-based Aleatoric Uncertainty Quantification for Cross-modal Retrieval [139.21955930418815]
  Cross-modal Retrieval methods build similarity relations between vision and language modalities by jointly learning a common representation space. However, the predictions are often unreliable due to the Aleatoric uncertainty, which is induced by low-quality data, e.g., corrupt images, fast-paced videos, and non-detailed texts. We propose a novel Prototype-based Aleatoric Uncertainty Quantification (PAU) framework to provide trustworthy predictions by quantifying the uncertainty arisen from the inherent data ambiguity.
  arXiv  Detail & Related papers  (2023-09-29T09:41:19Z)
• Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models [49.81937966106691]
  We develop a suite of non-asymptotic theory towards understanding the data generation process of diffusion models. In contrast to prior works, our theory is developed based on an elementary yet versatile non-asymptotic approach.
  arXiv  Detail & Related papers  (2023-06-15T16:30:08Z)
• A Convergence Theory for Federated Average: Beyond Smoothness [28.074273047592065]
  Federated learning enables a large amount of edge computing devices to learn a model without data sharing jointly. As a leading algorithm in this setting, Federated Average FedAvg, which runs Gradient Descent (SGD) in parallel on local devices, has been widely used. This paper provides a theoretical convergence study on Federated Learning.
  arXiv  Detail & Related papers  (2022-11-03T04:50:49Z)
• On the Unreasonable Effectiveness of Federated Averaging with Heterogeneous Data [39.600069116159695]
  Existing theory predicts that data heterogeneity will degrade the performance of the Federated Averaging (FedAvg) algorithm in federated learning. This paper explains the seemingly unreasonable effectiveness of FedAvg that contradicts the previous theoretical predictions.
  arXiv  Detail & Related papers  (2022-06-09T18:25:25Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.