Noisy tensor completion for tensors with a sparse canonical polyadic factor

“To be considered for the 2017 IEEE Jack Keil Wolf ISIT Student Paper Award.” In this paper we study the problem of noisy tensor completion for tensors that admit a canonical polyadic or CANDE-COMP/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.