Misclassification excess risk bounds for PAC-Bayesian classification via convexified loss
Abstract
PAC-Bayesian bounds have proven to be a valuable tool for deriving generalization bounds and for designing new learning algorithms in machine learning. However, it typically focus on providing generalization bounds with respect to a chosen loss function. In classification tasks, due to the non-convex nature of the 0-1 loss, a convex surrogate loss is often used, and thus current PAC-Bayesian bounds are primarily specified for this convex surrogate. This work shifts its focus to providing misclassification excess risk bounds for PAC-Bayesian classification when using a convex surrogate loss. Our key ingredient here is to leverage PAC-Bayesian relative bounds in expectation rather than relying on PAC-Bayesian bounds in probability. We demonstrate our approach in several important applications.
Cite
@article{arxiv.2408.08675,
title = {Misclassification excess risk bounds for PAC-Bayesian classification via convexified loss},
author = {The Tien Mai},
journal= {arXiv preprint arXiv:2408.08675},
year = {2024}
}