Broadcasted Nonparametric Tensor Regression

Abstract

Uncovering relationships among different variables from tensor data often lead to enhanced understanding of scientific and engineering problems. One recent statistical development under this setup is tensor regression. Most of the works make a strong assumption that the tensor covariates enter the model linearly, which is rather restrictive. Those models that consider the nonlinearity suffer from the curse of dimensionality and possess very weak interpretability. Motivated by observations from many real life applications and the need for nonlinearity, we propose a nonparametric tensor regression with broadcasting structure. Within the proposed model framework, we develop both an alternating updating algorithm as well as the asymptotic convergence rate for the proposed estimation. Through experiments on the synthetic data and two real data, we demonstrate the power of the proposed broadcasted nonparametric tensor regression.