Information-Theoretic Generalization Bounds for SGLD via Data-Dependent Estimates

By Jeffrey Negrea, Mahdi Haghifam, Gintare Karolina Dziugaite, Ashish J. Khisti, Daniel M. Roy. 2019

172 citations recorded by the source corpus.

In this work, we improve upon the stepwise analysis of noisy iterative learning algorithms initiated by Pensia, Jog, and Loh (2018) and recently extended by Bu, Zou, and Veeravalli (2019). Our main contributions are significantly improved mutual information bounds for Stochastic Gradient Langevin Dynamics via data-dependent estimates. Our approach is based on the variational characterization of mutual information and the use of data-dependent priors that forecast the mini-batch gradient based on a subset of the training samples. Our approach is broadly applicable within the information-theoretic framework of Russo and Zou (2015) and Xu and Raginsky (2017). Our bound can be tied to a measure of flatness of the empirical risk surface. As compared with other bounds that depend on the squared norms of gradients, empirical investigations show that the terms in our bounds are orders of magnitude smaller.

Subfields: Artificial Intelligence

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Citations in the corpus

Where is the Information in a Deep Neural Network? (2019, methodology): “(Russo & Zou, 2019; Xu & Raginsky, 2017; Pensia et al., 2018; Negrea et al., 2019; Asadi et al., 2018) bound the generalization gap of a training algorithm using the Shannon Information in the weights and a notion of “information stability”.”
User-friendly introduction to PAC-Bayes bounds (2021, methodology): “3 in [143], Negrea, Haghifam, Dziugaite, Khisti and Roy write explicitely the connection between MI bounds and PAC-Bayes bounds.”