PAC-Bayes bounds for stable algorithms with instance-dependent priors
Abstract
PAC-Bayes bounds have been proposed to get risk estimates based on a training sample. In this paper the PAC-Bayes approach is combined with stability of the hypothesis learned by a Hilbert space valued algorithm. The PAC-Bayes setting is used with a Gaussian prior centered at the expected output. Thus a novelty of our paper is using priors defined in terms of the data-generating distribution. Our main result estimates the risk of the randomized algorithm in terms of the hypothesis stability coefficients. We also provide a new bound for the SVM classifier, which is compared to other known bounds experimentally. Ours appears to be the first stability-based bound that evaluates to non-trivial values.
Cite
@article{arxiv.1806.06827,
title = {PAC-Bayes bounds for stable algorithms with instance-dependent priors},
author = {Omar Rivasplata and Emilio Parrado-Hernandez and John Shawe-Taylor and Shiliang Sun and Csaba Szepesvari},
journal= {arXiv preprint arXiv:1806.06827},
year = {2018}
}
Comments
16 pages, discussion of theory and experiments in the main body, detailed proofs and experimental details in the appendices