利用PAC-Bayes理论和Gibbs分布进行具有复杂度度量的泛化界限

Feb, 2024

利用PAC-Bayes理论和Gibbs分布进行具有复杂度度量的泛化界限

Leveraging PAC-Bayes Theory and Gibbs Distributions for Generalization Bounds with Complexity Measures

Paul Viallard, Rémi Emonet, Amaury Habrard, Emilie Morvant, Valentina Zantedeschi

TL;DR该研究利用分解的PAC-Bayes边界框架得出一个可适配任意复杂度度量的一般泛化边界，其中关键步骤是考虑一系列常用的分布：Gibbs分布。该边界在概率上同时适用于假设和学习样本，允许复杂度根据泛化差距进行调整，以适应假设类和任务。

Abstract

In statistical learning theory, a generalization bound usually involves a complexity measure imposed by the considered theoretical framework. This limits the scope of such bounds, as other forms of capacity measu