Talker:  Taiji Suzuki (TIT)

Title: Risk bounds of convex and Bayes tensor estimators: near optimal rate without strong convexity

Abstract: Low rank tensor estimation is a useful statistical tool to analyze multi-dimensional array data such as spatio-temporal data and purchase data. We develop two types of estimators for estimating a low rank tensor: minimum convex regularized risk minimizer and Bayes estimator. We show the statistical convergence rates of these methods. In particular, the Bayes estimator achieves near optimal rate without restricted strong convexity on the design. This talk partly includes collaborations with Ryota Tomioka.