# Higher-Order Low-Rank Regression

arXiv: https://arxiv.org/abs/1602.06863 · HTML: https://mlsanity.com/paper/1602.06863/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Feb 2016.

## Built on by (most cited first, 1 of 1)

- [Bayesian longitudinal tensor response regression for modeling neuroplasticity](https://mlsanity.com/paper/2309.10065/) (2023)

## Abstract (arXiv)

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.