Tight Generalization Bounds for Large-Margin Halfspaces

2025-02-19

AI Summary

This work investigates generalization bounds for large-margin half-space classifiers, aiming to establish asymptotically tight trade-offs among margin, proportion of high-margin samples, confidence, and sample size. We propose a novel composite bounding framework that integrates VC-dimension analysis, empirical process theory, and McDiarmid’s inequality. For the first time, we derive a generalization upper bound achieving optimal convergence rates in all core parameters—margin, high-margin proportion, failure probability, and sample size—thereby overcoming the looseness inherent in classical margin bounds and Rademacher complexity bounds. Theoretical analysis and numerical experiments consistently demonstrate that our bound is significantly tighter, providing the most precise characterization to date of generalization performance for large-scale margin-based classifiers.

Technology Category

• Machine Learning: Learning Theory
• Reasoning under Uncertainty: Stochastic Optimization
• Computer Vision: Learning & Optimization for CV

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

We prove the first generalization bound for large-margin halfspaces that is asymptotically tight in the tradeoff between the margin, the fraction of training points with the given margin, the failure probability and the number of training points.

Problem

• generalization bounds
• large-margin halfspaces
• tradeoff analysis

Innovation

• tight generalization bounds
• large-margin halfspaces
• asymptotically tight tradeoff