CP Degeneracy in Tensor Regression Academic Article

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) $M$-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.

authors

• Wong, Raymond Ka Wai

author list (cited authors)

• Zhou, Y. a., Wong, R., & He, K.

complete list of authors

• Zhou, Ya||Wong, Raymond KW||He, Kejun

publication date

• October 2020

keywords

• Cs.lg
• Stat.me
• Stat.ml

URL

• http://dx.doi.org/10.1109/ACCESS.2021.3049494