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

Konstantinos Pitas
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:7739-7749, 2020.

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.

Cite this Paper

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.} }
Endnote
%0 Conference Paper %T Dissecting Non-Vacuous Generalization Bounds based on the Mean-Field Approximation %A Konstantinos Pitas %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-pitas20a %I PMLR %P 7739--7749 %U https://proceedings.mlr.press/v119/pitas20a.html %V 119 %X 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.
APA
Pitas, K.. (2020). Dissecting Non-Vacuous Generalization Bounds based on the Mean-Field Approximation. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:7739-7749 Available from https://proceedings.mlr.press/v119/pitas20a.html.

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