Broadcasted Nonparametric Tensor Regression

Understand

We propose a novel use of a broadcasting operation, which distributes univariate functions to all entries of the tensor covariate, to model the nonlinearity in tensor regression nonparametrically.

• A penalized estimation and the corresponding algorithm are proposed.
• Our theoretical investigation, which allows the dimensions of the tensor covariate to diverge, indicates that the proposed estimation yields a desirable convergence rate.
• We also provide a minimax lower bound, which characterizes the optimality of the proposed estimator for a wide range of scenarios.