  We propose a set of convex low rank inducing norms for a coupled matrices and
tensors (hereafter coupled tensors), which shares information between matrices
and tensors through common modes. More specifically, we propose a mixture of
the overlapped trace norm and the latent norms with the matrix trace norm, and
then, we propose a new completion algorithm based on the proposed norms. A key
advantage of the proposed norms is that it is convex and can find a globally
optimal solution, while existing methods for coupled learning are non-convex.
Furthermore, we analyze the excess risk bounds of the completion model
regularized by our proposed norms which show that our proposed norms can
exploit the low rankness of coupled tensors leading to better bounds compared
to uncoupled norms. Through synthetic and real-world data experiments, we show
that the proposed completion algorithm compares favorably with existing
completion algorithms.
