SILO



The weekly SILO Seminar Series is made possible through the generous support of the 3M Company and its Advanced Technology Group

3M

with additional support from the Analytics Group of the Northwestern Mutual Life Insurance Company

Northwestern Mutual

Information theoretic perspectives on learning algorithms

Varun Jog ,

Date and Time: Feb 07, 2018 (12:30 PM)
Location: Orchard room (3280) at the Wisconsin Institute for Discovery Building

Abstract:

Abstract:
In statistical learning theory, generalization error is used to quantify the degree to which a supervised machine learning algorithm may overfit to training data. We overview some recent work [Xu and Raginsky (2017)] that bounds generalization error of empirical risk minimization based on the mutual information I(S;W) between the algorithm input S and the algorithm output W. We leverage these results to derive generalization error bounds for a broad class of iterative algorithms that are characterized by bounded, noisy updates with Markovian structure, such as stochastic gradient Langevin dynamics (SGLD). We describe certain shortcomings of mutual information-based bounds, and propose alternate bounds that employ the Wasserstein metric from optimal transport theory. We compare the Wasserstein metric-based bounds with the mutual information-based bounds and show that for a class of data generating distributions, the former leads to stronger
bounds on the generalization error.

This is joint work with Adrian Tovar-Lopez, Ankit Pensia, and Po-Ling Loh.