Tensor Completion via Gaussian Process Based Initialization

TL;DR

This paper introduces a Gaussian Process-based initialization method for tensor completion in the tensor train format, improving reconstruction accuracy and automatically selecting tensor ranks, especially for high-dimensional data generated by smooth functions.

Contribution

It proposes a novel initialization scheme combining Gaussian Process Regression and TT-cross approximation for tensor completion, enhancing accuracy and rank selection.

Findings

Improved reconstruction error over random initialization

Automatic rank determination via TT-cross approximation

Effective for high-dimensional tensors generated by smooth functions

Abstract

In this paper, we consider the tensor completion problem representing the solution in the tensor train (TT) format. It is assumed that tensor is high-dimensional, and tensor values are generated by an unknown smooth function. The assumption allows us to develop an efficient initialization scheme based on Gaussian Process Regression and TT-cross approximation technique. The proposed approach can be used in conjunction with any optimization algorithm that is usually utilized in tensor completion problems. We empirically justify that in this case the reconstruction error improves compared to the tensor completion with random initialization. As an additional benefit, our technique automatically selects rank thanks to using the TT-cross approximation technique.