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[2501.10538] Universality of Benign Overfitting in Binary Linear Classification
Summary
This article explores the phenomenon of benign overfitting in binary linear classification, revealing new insights into its occurrence in noisy environments and expanding the theoretical understanding of maximum margin classifiers.
Why It Matters
Understanding benign overfitting is crucial for improving machine learning models, particularly in scenarios where data is noisy. This research broadens the applicability of benign overfitting concepts, potentially enhancing model performance across various statistical models and real-world applications.
Key Takeaways
- Benign overfitting allows deep learning models to generalize well despite fitting noisy data.
- The study identifies a phase transition in test error bounds for noisy models, enhancing theoretical understanding.
- Relaxed assumptions on covariate distributions expand the scenarios where benign overfitting applies.
Computer Science > Machine Learning arXiv:2501.10538 (cs) [Submitted on 17 Jan 2025 (v1), last revised 24 Feb 2026 (this version, v2)] Title:Universality of Benign Overfitting in Binary Linear Classification Authors:Ichiro Hashimoto, Stanislav Volgushev, Piotr Zwiernik View a PDF of the paper titled Universality of Benign Overfitting in Binary Linear Classification, by Ichiro Hashimoto and 2 other authors View PDF Abstract:The practical success of deep learning has led to the discovery of several surprising phenomena. One of these phenomena, that has spurred intense theoretical research, is ``benign overfitting'': deep neural networks seem to generalize well in the over-parametrized regime even though the networks show a perfect fit to noisy training data. It is now known that benign overfitting also occurs in various classical statistical models. For linear maximum margin classifiers, benign overfitting has been established theoretically in a class of mixture models with very strong assumptions on the covariate distribution. However, even in this simple setting, many questions remain open. For instance, most of the existing literature focuses on the noiseless case where all true class labels are observed without errors, whereas the more interesting noisy case remains poorly understood. We provide a comprehensive study of benign overfitting for linear maximum margin classifiers. We discover a phase transition in test error bounds for the noisy model which was previously un...