  In this paper we study the problem of noisy tensor completion for tensors
that admit a canonical polyadic or CANDECOMP/PARAFAC (CP) decomposition with
one of the factors being sparse. We present general theoretical error bounds
for an estimate obtained by using a complexity-regularized maximum likelihood
principle and then instantiate these bounds for the case of additive white
Gaussian noise. We also provide an ADMM-type algorithm for solving the
complexity-regularized maximum likelihood problem and validate the theoretical
finding via experiments on synthetic data set.
