Efficient Convex Completion of Coupled Tensors using Coupled Nuclear Norms

Coupled norms have emerged as a convex method to solve coupled tensor com-
pletion. A limitation with coupled norms is that they only induce low-rankness
using the multilinear rank of coupled tensors. In this paper, we introduce a new
set of coupled norms known as coupled nuclear norms by constraining the CP
rank of coupled tensors. We propose new coupled completion models using the
coupled nuclear norms as regularizers, which can be optimized using computa-
tionally efficient optimization methods. We derive excess risk bounds for pro-
posed coupled completion models and show that proposed norms lead to better
performance. Through simulation and real-data experiments, we demonstrate that
proposed norms achieve better performance for coupled completion compared to
existing coupled norms.