Nonnegative Tensor Completion via Integer Optimization
Abstract
Unlike matrix completion, tensor completion does not have an algorithm that is known to achieve the information-theoretic sample complexity rate. This paper develops a new algorithm for the special case of completion for nonnegative tensors. We prove that our algorithm converges in a linear (in numerical tolerance) number of oracle steps, while achieving the information-theoretic rate. Our approach is to define a new norm for nonnegative tensors using the gauge of a particular 0-1 polytope; integer linear programming can, in turn, be used to solve linear separation problems over this polytope. We combine this insight with a variant of the Frank-Wolfe algorithm to construct our numerical algorithm, and we demonstrate its effectiveness and scalability through computational experiments using a laptop on tensors with up to one-hundred million entries.
Cite
@article{arxiv.2111.04580,
title = {Nonnegative Tensor Completion via Integer Optimization},
author = {Caleb Bugg and Chen Chen and Anil Aswani},
journal= {arXiv preprint arXiv:2111.04580},
year = {2022}
}