A New Convex Relaxation for Tensor Completion
This work addresses tensor completion, a problem in machine learning and data analysis, with incremental improvements over prior methods.
The paper tackles the problem of learning a tensor from linear measurements by proposing a new convex relaxation on the Euclidean ball to address limitations of existing tensor trace norm regularization, resulting in significant improvements in estimation error on synthetic and real datasets.
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.