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

## TL;DR

This paper addresses noisy tensor completion for tensors with a sparse CP decomposition, providing theoretical error bounds, an ADMM algorithm, and experimental validation on synthetic data.

## Contribution

It introduces a novel approach combining complexity-regularized maximum likelihood with theoretical error bounds for tensors with sparse factors.

## Key findings

- Theoretical error bounds for noisy tensor completion.
- An ADMM algorithm for practical implementation.
- Validation of theoretical results on synthetic datasets.

## Abstract

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.