ICML 2020poster11 citations

Dissecting Non-Vacuous Generalization Bounds based on the Mean-Field Approximation

Konstantinos Pitas

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.}
}
Dissecting Non-Vacuous Generalization Bounds based on the Mean-Field Approximation · ICML 2020