  Low-Rank Tensor Completion, a method which exploits the inherent structure of
tensors, has been studied extensively as an effective approach to tensor
completion. Whilst such methods attained great success, none have
systematically considered exploiting the numerical priors of tensor elements.
Ignoring numerical priors causes loss of important information regarding the
data, and therefore prevents the algorithms from reaching optimal accuracy.
Despite the existence of some individual works which consider ad hoc numerical
priors for specific tasks, no generalizable frameworks for incorporating
numerical priors have appeared. We present the Generalized CP Decomposition
Tensor Completion (GCDTC) framework, the first generalizable framework for
low-rank tensor completion that takes numerical priors of the data into
account. We test GCDTC by further proposing the Smooth Poisson Tensor
Completion (SPTC) algorithm, an instantiation of the GCDTC framework, whose
performance exceeds current state-of-the-arts by considerable margins in the
task of non-negative tensor completion, exemplifying GCDTC's effectiveness. Our
code is open-source.
