Noisy Tensor Completion for Tensors With a Sparse Canonical Polyadic Factor



Noisy Tensor Completion for Tensors With a Sparse Canonical Polyadic Factor

Noisy Tensor Completion for Tensors With a Sparse Canonical Polyadic Factor
Research Paper / IEEE International Symposium on Information Theory (ISIT) / Feb 2017 / Image Processing, Machine/Deep Learning/AI

“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.