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Title: Estimation accuracy and computational efficiency of non-parametric kernel tensor estimators Authors:  Taiji Suzuki - University of Tokyo / RIKEN-AIP (Japan) [presenting]
Abstract: A problem of estimating a low rank tensor in infinite dimensional Hilbert spaces is considered, and the statistical properties and computational efficiency of some estimators is discussed. There are wide applications of estimating low rank tensors, for example, recommendation system, spatio-temporal data analysis, and multi-task learning. The tensor model we consider consists of the sum of products of functions in Reproducing Kernel Hilbert Spaces (RKHSs) defined on the input data sources. To estimate the nonparametric model, we consider a Bayes estimator and an empirical risk minimizer computed by an alternating minimization method. Then, we discuss the trade-off between the statistical performances and the computational efficiency by showing some theoretical and numerical results. In the theoretical analysis, we give upper bounds of the risks and show the minimax optimal rate.