A New Convex Relaxation for Tensor Completion

TL;DR

This paper introduces a novel convex relaxation method for tensor completion that outperforms traditional trace norm regularization in accuracy and remains computationally feasible, demonstrated through experiments on synthetic and real datasets.

Contribution

The paper proposes an alternative convex relaxation for tensor learning that addresses limitations of trace norm regularization and provides an efficient solution technique.

Findings

Significant reduction in estimation error compared to tensor trace norm regularization

Method remains computationally tractable for practical datasets

Improved performance demonstrated on synthetic and real datasets

Abstract

We study the problem of learning a tensor from a set of linear measurements. A prominent methodology for this problem is based on a generalization of trace norm regularization, which has been used extensively for learning low rank matrices, to the tensor setting. In this paper, we highlight some limitations of this approach and propose an alternative convex relaxation on the Euclidean ball. We then describe a technique to solve the associated regularization problem, which builds upon the alternating direction method of multipliers. Experiments on one synthetic dataset and two real datasets indicate that the proposed method improves significantly over tensor trace norm regularization in terms of estimation error, while remaining computationally tractable.