Broadcasted Nonparametric Tensor Regression

We propose a novel broadcasting idea to model the nonlinearity in tensor regression non-parametrically. Unlike existing non-parametric tensor regression models, the resulting model strikes a good balance between flexibility and interpretability. A penalized estimation and corresponding algorithm are proposed. Our theoretical investigation, which allows the dimensions of the tensor covariate to diverge, indicates that the proposed estimation enjoys desirable convergence rate. Numerical experiments are conducted to confirm the theoretical finding and show that the proposed model has advantage over existing linear counterparts.