PAC-Bayes with Backprop
Abstract
We explore the family of methods "PAC-Bayes with Backprop" (PBB) to train probabilistic neural networks by minimizing PAC-Bayes bounds. We present two training objectives, one derived from a previously known PAC-Bayes bound, and a second one derived from a novel PAC-Bayes bound. Both training objectives are evaluated on MNIST and on various UCI data sets. Our experiments show two striking observations: we obtain competitive test set error estimates (~1.4% on MNIST) and at the same time we compute non-vacuous bounds with much tighter values (~2.3% on MNIST) than previous results. These observations suggest that neural nets trained by PBB may lead to self-bounding learning, where the available data can be used to simultaneously learn a predictor and certify its risk, with no need to follow a data-splitting protocol.
Cite
@article{arxiv.1908.07380,
title = {PAC-Bayes with Backprop},
author = {Omar Rivasplata and Vikram M Tankasali and Csaba Szepesvari},
journal= {arXiv preprint arXiv:1908.07380},
year = {2019}
}