ICML 2020poster11 citations
Dissecting Non-Vacuous Generalization Bounds based on the Mean-Field Approximation
Abstract
Explaining how overparametrized neural networks simultaneously achieve low risk and zero empirical risk on benchmark datasets is an open problem. PAC-Bayes bounds optimized using variational inference (VI) have been recently proposed as a promising direction in obtaining non-vacuous bounds. We show empirically that this approach gives negligible gains when modelling the posterior as a Gaussian with diagonal covariance—known as the mean-field approximation. We investigate common explanations, such as the failure of VI due to problems in optimization or choosing a suboptimal prior. Our results suggest that investigating richer posteriors is the most promising direction forward.
BibTeX
@InProceedings{pmlr-v119-pitas20a,
title = {Dissecting Non-Vacuous Generalization Bounds based on the Mean-Field Approximation},
author = {Pitas, Konstantinos},
booktitle = {Proceedings of the 37th International Conference on Machine Learning},
pages = {7739--7749},
year = {2020},
editor = {III, Hal Daumé and Singh, Aarti},
volume = {119},
series = {Proceedings of Machine Learning Research},
month = {13--18 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v119/pitas20a/pitas20a.pdf},
url = {https://proceedings.mlr.press/v119/pitas20a.html},
abstract = {Explaining how overparametrized neural networks simultaneously achieve low risk and zero empirical risk on benchmark datasets is an open problem. PAC-Bayes bounds optimized using variational inference (VI) have been recently proposed as a promising direction in obtaining non-vacuous bounds. We show empirically that this approach gives negligible gains when modelling the posterior as a Gaussian with diagonal covariance—known as the mean-field approximation. We investigate common explanations, such as the failure of VI due to problems in optimization or choosing a suboptimal prior. Our results suggest that investigating richer posteriors is the most promising direction forward.}
}