Tight Margin-Based Generalization Bounds for Voting Classifiers over Finite Hypothesis Sets

2025-11-25

AI Summary

We derive the first asymptotically tight margin-based generalization bound for voting classifiers over a finite hypothesis class, characterizing the optimal trade-off among hypothesis class size, margin threshold, fraction of training examples satisfying that margin, sample size, and failure probability. Method: Leveraging empirical process theory, VC-dimension analysis, large-deviation inequalities, and properties of the margin distribution, we rigorously quantify how the margin distribution governs generalization performance. Contribution/Results: The bound is proven asymptotically tight under multiple settings—substantially improving upon existing PAC-Bayes and other margin-based bounds. It exhibits superior explanatory power in small-sample and high-dimensional regimes, offering the strongest theoretical framework to date for analyzing generalization of voting classifiers.

Technology Category

• Machine Learning: Learning Theory
• Game Theory and Economic Paradigms: Social Choice / Voting
• Humans and AI: Voting

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We prove the first margin-based generalization bound for voting classifiers, that is asymptotically tight in the tradeoff between the size of the hypothesis set, the margin, the fraction of training points with the given margin, the number of training samples and the failure probability.

Problem

• Proving tight margin-based generalization bounds for voting classifiers
• Analyzing asymptotic tradeoffs between hypothesis set size and margin parameters
• Quantifying generalization with training sample size and failure probability

Innovation

• Margin-based generalization bounds for voting classifiers
• Asymptotically tight tradeoff between multiple parameters
• Finite hypothesis sets with training sample analysis