# Noisy Tensor Completion for Tensors with a Sparse Canonical Polyadic Factor

arXiv: https://arxiv.org/abs/1704.02534 · HTML: https://mlsanity.com/paper/1704.02534/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2017.

## Built on by (most cited first, 1 of 1)

- [Tensor Completion via Integer Optimization](https://mlsanity.com/paper/2402.05141/) (2024)

## Abstract (arXiv)

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.