Bayes method for low rank tensor estimation

International Meeting on High-Dimensional Data-Driven Science 2015

Suzuki, Taiji^1,2 ; Kanagawa, Heishiro^1

Graduate School of Information Science and Engineering, Tokyo Institute of Technology, O-okayama 2-12-1, Meguro-ku, Tokyo

152-8552, Japan^1

PRESTO, JST, Japan^2

关键词: Multitask learning;    Nonlinear functions;    Predictive accuracy;    Regression coefficient;    Regression problem;    Spatio-temporal data;    Statistical convergence;    Strong convexities;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/699/1/012020/pdf
DOI  :  10.1088/1742-6596/699/1/012020

来源: IOP

【 摘 要 】

We investigate the statistical convergence rate of a Bayesian low-rank tensor estimator, and construct a Bayesian nonlinear tensor estimator. The 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 extend the tensor estimator to a nonlinear function estimator so that we estimate a function that is a tensor product of several functions.