Higher-Order Low-Rank Regression

TL;DR

This paper introduces HOLRR, an efficient algorithm for tensor-structured regression that minimizes least squares under multilinear rank constraints, offering theoretical guarantees and outperforming existing methods in speed and accuracy.

Contribution

The paper presents HOLRR, a novel algorithm for tensor regression with theoretical guarantees, and extends it with a kernel version, improving efficiency and performance.

Findings

HOLRR outperforms multivariate and multilinear regression methods.

HOLRR is significantly faster than existing tensor methods.

Experiments demonstrate HOLRR's effectiveness on synthetic and real data.

Abstract

This paper proposes an efficient algorithm (HOLRR) to handle regression tasks where the outputs have a tensor structure. We formulate the regression problem as the minimization of a least square criterion under a multilinear rank constraint, a difficult non convex problem. HOLRR computes efficiently an approximate solution of this problem, with solid theoretical guarantees. A kernel extension is also presented. Experiments on synthetic and real data show that HOLRR outperforms multivariate and multilinear regression methods and is considerably faster than existing tensor methods.