arxiv_ml 88% Match Research Paper Machine learning theorists,Researchers in statistical learning,Developers focused on model robustness 1 week ago

A Framework for Bounding Deterministic Risk with PAC-Bayes: Applications to Majority Votes

ai-safety › robustness

📄 Abstract

Abstract: PAC-Bayes is a popular and efficient framework for obtaining generalization guarantees in situations involving uncountable hypothesis spaces. Unfortunately, in its classical formulation, it only provides guarantees on the expected risk of a randomly sampled hypothesis. This requires stochastic predictions at test time, making PAC-Bayes unusable in many practical situations where a single deterministic hypothesis must be deployed. We propose a unified framework to extract guarantees holding for a single hypothesis from stochastic PAC-Bayesian guarantees. We present a general oracle bound and derive from it a numerical bound and a specialization to majority vote. We empirically show that our approach consistently outperforms popular baselines (by up to a factor of 2) when it comes to generalization bounds on deterministic classifiers.

Authors (2)

Benjamin Leblanc

Pascal Germain

Submitted

October 29, 2025

arXiv Category

cs.LG

arXiv PDF

Key Contributions

This paper proposes a unified framework to derive generalization guarantees for single, deterministic hypotheses from stochastic PAC-Bayesian bounds. It presents a general oracle bound and a numerical bound, specialized for majority vote classifiers, which empirically outperform popular baselines for generalization bounds on deterministic classifiers.

Business Value

Provides stronger theoretical assurances for the generalization performance of deployed models, increasing confidence in their reliability and robustness in real-world applications.

Paper Metadata

Innovation Type

Theoretical Innovation

Deployment Feasibility

High. The theoretical framework enables more reliable deployment of deterministic models by providing stronger generalization bounds.

Limitations Addressed

Classical PAC-Bayes provides guarantees only on expected risk of random hypotheses (requiring stochastic predictions),Inability to use PAC-Bayes for deploying single deterministic hypotheses in practice

Performance Gains

Consistently outperforms popular baselines for generalization bounds on deterministic classifiers

Technical Tags

PAC-Bayesgeneralization guaranteesdeterministic hypothesisstochastic predictionsoracle boundnumerical boundmajority votehypothesis spaceexpected riskdeterministic classifiers

Research Topics

Machine Learning TheoryStatistical Learning TheoryRobustnessGeneralization Bounds

Methods & Architectures

Unified PAC-Bayes frameworkDerivation of oracle and numerical boundsSpecialization to majority vote

Applications & Tasks

Supervised Learning Classification GeneralizationRisk Bounding Extracting deterministic hypothesis guarantees from PAC-BayesBounding generalization risk for single hypotheses

Datasets & Benchmarks

Benchmarks

Up to a factor of 2 improvement over popular baselines

Related Fields

Machine Learning TheoryStatistical InferenceOptimizationTheoretical Computer Science

Keywords

PAC-Bayesgeneralizationdeterministicstochasticboundhypothesisriskmajority votemachine learning theoryrobustness

Academic Context

#Machine Learning Theory#Statistical Learning Theory#Robustness#Generalization Bounds

Commercial Potential

Potential Products

Tools for generating stronger generalization boundsLibraries for robust model deployment

Target Industries

TechnologyFinanceHealthcareAny industry requiring reliable ML models

Use Case Examples

Providing stronger theoretical guarantees for a deployed spam filter.Ensuring a medical diagnostic model generalizes well to unseen patient data.

Competitive Edge

Extends PAC-Bayes theory to provide practical guarantees for deterministic classifiers, overcoming a key limitation of the classical framework and offering superior bounds.

Resource Requirements

Compute Needs

Low, primarily theoretical analysis and simulation for empirical validation.

Data Requirements

Standard datasets for classification tasks to empirically validate bounds.

Deployment Constraints

Theoretical nature may require careful interpretation for practical application

Scalability

The theoretical framework itself is not directly about computational scalability but about the quality of generalization bounds.

Production Readiness

Maturity Level

Research

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