Tensor-on-tensor regression. We propose a framework for the linear prediction of a multi-way array (i.e., a tensor) from another multi-way array of arbitrary dimension, using the contracted tensor product. This framework generalizes several existing approaches, including methods to predict a scalar outcome from a tensor, a matrix from a matrix, or a tensor from a scalar. We describe an approach that exploits the multiway structure of both the predictors and the outcomes by restricting the coefficients to have reduced CP-rank. We propose a general and efficient algorithm for penalized least-squares estimation, which allows for a ridge (L_2) penalty on the coefficients. The objective is shown to give the mode of a Bayesian posterior, which motivates a Gibbs sampling algorithm for inference. We illustrate the approach with an application to facial image data. An R package is available at

Keywords for this software

Anything in here will be replaced on browsers that support the canvas element

References in zbMATH (referenced in 1 article )

Showing result 1 of 1.
Sorted by year (citations)

  1. Pan, Yuqing; Mai, Qing; Zhang, Xin: Covariate-adjusted tensor classification in high dimensions (2019)