Bayes Estimation of High Dimensional Tensors

Abstract

Low rank tensor estimation has a lot of applications such as recommendation system, spatiotemporal data analysis, and multi-task learning. We consider a Bayes estimator for this problem. We give theoretical analyses for the Bayes estimator and show that the Bayes estimator achieves the minimax optimal predictive accuracy. We also consider a nonparametric tensor model and a Bayes estimator for that model. It is also shown that the Bayes estimator of the nonparametric model achieves the minimax optimality. Finally, numerical experiments were conducted on restaurant evaluation data and give comparison with the Bayes estimators and other methods.