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Noisy Tensor Completion for Tensors with a Sparse Canonical Polyadic Factor

Abstract · Apr 8, 2017 20:17 ·

tensor completion noisy tensors sparse decomposition regularized estimate stat-ml

Arxiv Abstract

  • Swayambhoo Jain
  • Alexander Gutierrez
  • Jarvis Haupt

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.

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