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arXiv · 2111.04580

Nonnegative Tensor Completion via Integer Optimization

Caleb Bugg·Chen Chen·Anil Aswani
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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.

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BibTeXRIS

Caleb Bugg, Chen Chen, Anil Aswani. 2021-11-08. Nonnegative Tensor Completion via Integer Optimization. https://arxiv.org/abs/2111.04580

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