Noisy Tensor Completion for Tensors with a Sparse Canonical Polyadic Factor
This work addresses tensor completion for a specific structural case, which is incremental as it builds on existing CP decomposition methods by incorporating sparsity constraints.
The paper tackles noisy tensor completion for tensors with a sparse CP factor, deriving theoretical error bounds for an estimate using complexity-regularized maximum likelihood and validating them with experiments on synthetic data.
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.