Data-dependent PAC-Bayes priors via differential privacy
Abstract
The Probably Approximately Correct (PAC) Bayes framework (McAllester, 1999) can incorporate knowledge about the learning algorithm and (data) distribution through the use of distribution-dependent priors, yielding tighter generalization bounds on data-dependent posteriors. Using this flexibility, however, is difficult, especially when the data distribution is presumed to be unknown. We show how an {\epsilon}-differentially private data-dependent prior yields a valid PAC-Bayes bound, and then show how non-private mechanisms for choosing priors can also yield generalization bounds. As an application of this result, we show that a Gaussian prior mean chosen via stochastic gradient Langevin dynamics (SGLD; Welling and Teh, 2011) leads to a valid PAC-Bayes bound given control of the 2-Wasserstein distance to an {\epsilon}-differentially private stationary distribution. We study our data-dependent bounds empirically, and show that they can be nonvacuous even when other distribution-dependent bounds are vacuous.
Cite
@article{arxiv.1802.09583,
title = {Data-dependent PAC-Bayes priors via differential privacy},
author = {Gintare Karolina Dziugaite and Daniel M. Roy},
journal= {arXiv preprint arXiv:1802.09583},
year = {2019}
}
Comments
18 pages, 2 figures; equivalent to camera ready, but includes supplementary materials; subsumes and extends some results first reported in arXiv:1712.09376