Data-dependent PAC-Bayes priors via differential privacy

Part of Advances in Neural Information Processing Systems 31 (NeurIPS 2018)

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Gintare Karolina Dziugaite, Daniel M. Roy


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 a 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 due to control of the 2-Wasserstein distance to a 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.