Tensor regression is an important and useful tool for analyzing multidimensional array data. To deal with high dimensionality, CANDECOMP/PARAFAC (CP) low-rank constraints are often imposed on the coefficient tensor parameter in (penalized) loss functions. However, besides well-known non-identifiability issue of CP parameters, we demonstrate that corresponding optimization may not have any attai...

Abstract In this section we prove the non-degeneracy of solutions to one-phase problem ( 2.1 ). Our main result is following.