CP Degeneracy in Tensor Regression
Abstract
Tensor linear regression is an important and useful tool for analyzing tensor data. To deal with high dimensionality, CANDECOMP/PARAFAC (CP) low-rank constraints are often imposed on the coefficient tensor parameter in the (penalized) -estimation. However, we show that the corresponding optimization may not be attainable, and when this happens, the estimator is not well-defined. This is closely related to a phenomenon, called CP degeneracy, in low-rank tensor approximation problems. In this article, we provide useful results of CP degeneracy in tensor regression problems. In addition, we provide a general penalized strategy as a solution to overcome CP degeneracy. The asymptotic properties of the resulting estimation are also studied. Numerical experiments are conducted to illustrate our findings.
Cite
@article{arxiv.2010.13568,
title = {CP Degeneracy in Tensor Regression},
author = {Ya Zhou and Raymond K. W. Wong and Kejun He},
journal= {arXiv preprint arXiv:2010.13568},
year = {2024}
}