Revisiting Generalization for Deep Learning: PAC-Bayes, Flat Minima, and Generative Models

In this work, we construct generalization bounds to understand existing learning algorithms and propose new ones. Generalization bounds relate empirical performance to future expected performance. The tightness of these bounds vary widely, and depends on the complexity of the learning task and the amount of data available, but also on how much information the bounds take into consideration. We are particularly concerned with data and algorithm- dependent bounds that are quantitatively nonvacuous. We begin with an analysis of stochastic gradient descent (SGD) in supervised learning. By formalizing the notion of flat minima using PAC-Bayes generalization bounds, we obtain nonvacuous generalization bounds for stochastic classifiers based on SGD solutions. Despite strong empirical performance in many settings, SGD rapidly overfits in others. By combining nonvacuous generalization bounds and structural risk minimization, we arrive at an algorithm that trades-off accuracy and generalization guarantees. We also study generalization in the context of unsupervised learning. We propose to use a two sample test statistic for training neural network generator models and bound the gap between the population and the empirical estimate of the statistic.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2020

Author dc:creator

• Dziugaite, Gintare Karolina

Advisor dc:contributor.advisor

• Ghahramani, Zoubin

• Deep learning
• statistical learning theory
• Generalization in neural networks
• adversarial learning
• PAC-Bayesian bounds
• generative models

Licence

• https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/fe232f76-918b-4496-ad16-4a6c18d32f62/download
• https://www.rioxx.net/licenses/all-rights-reserved/

Language dc:language

en

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.40428

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/293273