Year: 2025
Type: conference-paper
Abstract: The tensor completion problem is to fill-in unobserved entries of a partially observed tensor. However, past approaches to tensor completion either achieved the information-theoretic rate but lacked practical algorithms, or proposed polynomial-time algorithms that require an exponentially-larger number of samples for low estimation error. In this paper, we develop a novel tensor completion algorithm to tackle this challenge by achieving both provable convergence (in numerical tolerance) in a linear number of oracle steps and the information-theoretic rate. We formulate tensor completion as a convex optimization problem constrained using a gauge-based tensor norm and provide proofs of properties of this norm including its computational complexity and tensor rank surrogacy. We formulate this norm such that linear separation problems over the gauge unit-ball can be solved using integer optimization. This enables the use of Frank-Wolfe variant to build our algorithm. We demonstrate effectiveness of our method using experiments with simulated data and with an application towards providing low-computation predictions of battery storage flows that may be beneficial in billion-device-scale integration of electromobility systems with the grid.
Language: English
Subfield: Computational Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7123349276