# Broadcasted Nonparametric Tensor Regression

arXiv: https://arxiv.org/abs/2008.12927 · HTML: https://mlsanity.com/paper/2008.12927/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Aug 2020.

## Built on by (most cited first, 2 of 2)

- [Nonparametric Trace Regression in High Dimensions via Sign Series Representation](https://mlsanity.com/paper/2105.01783/) (2021)
- [ANTLER: Bayesian Nonlinear Tensor Learning and Modeler for Unstructured, Varying-Size Point Cloud Data](https://mlsanity.com/paper/2202.13788/) (2022)

## Abstract (arXiv)

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. Numerical experiments are conducted to confirm the theoretical findings, and they show that the proposed model has advantages over its existing linear counterparts.