Convergence rate of Bayesian tensor estimator and its minimax optimality
published: Sept. 27, 2015, recorded: July 2015, views: 1527
Report a problem or upload filesIf you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
We investigate the statistical convergence rate of a Bayesian low-rank tensor estimator, and derive the minimax optimal rate for learning a low-rank tensor. Our problem setting is the regression problem where the regression coefficient forms a tensor structure. This problem setting occurs in many practical applications, such as collaborative filtering, multi-task learning, and spatio-temporal data analysis. The convergence rate of the Bayes tensor estimator is analyzed in terms of both in-sample and out-of-sample predictive accuracies. It is shown that a fast learning rate is achieved without any strong convexity of the observation. Moreover, we show that the method has adaptivity to the unknown rank of the true tensor, that is, the near optimal rate depending on the true rank is achieved even if it is not known a priori. Finally, we show the minimax optimal learning rate for the tensor estimation problem, and thus show that the derived bound of the Bayes estimator is tight and actually near minimax optimal.
Link this pageWould you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !