TY - DATA T1 - Tensor-on-Tensor Regression PY - 2018/06/06 AU - Eric F. Lock UR - https://tandf.figshare.com/articles/dataset/Tensor-on-tensor_regression/5573509 DO - 10.6084/m9.figshare.5573509.v2 L4 - https://ndownloader.figshare.com/files/9686887 L4 - https://ndownloader.figshare.com/files/9686890 KW - Multiway data KW - PARAFAC/CANDECOMP KW - Reduced rank regression KW - Ridge regression N2 - I propose a framework for the linear prediction of a multiway array (i.e., a tensor) from another multiway 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. I describe an approach that exploits the multiway structure of both the predictors and the outcomes by restricting the coefficients to have reduced PARAFAC/CANDECOMP rank. I propose a general and efficient algorithm for penalized least-squares estimation, which allows for a ridge (L2) penalty on the coefficients. The objective is shown to give the mode of a Bayesian posterior, which motivates a Gibbs sampling algorithm for inference. I illustrate the approach with an application to facial image data. An R package is available at https://github.com/lockEF/MultiwayRegression. ER -