Vector-Valued Least-Squares Regression under Output Regularity Assumptions
Machine Learning
2022-11-17 v1 Machine Learning
Abstract
We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study under which setting statistical performance is improved in comparison to full-rank method. Our analysis extends the interest of reduced-rank regression beyond the standard low-rank setting to more general output regularity assumptions. We illustrate our theoretical insights on synthetic least-squares problems. Then, we propose a surrogate structured prediction method derived from this reduced-rank method. We assess its benefits on three different problems: image reconstruction, multi-label classification, and metabolite identification.
Cite
@article{arxiv.2211.08958,
title = {Vector-Valued Least-Squares Regression under Output Regularity Assumptions},
author = {Luc Brogat-Motte and Alessandro Rudi and Céline Brouard and Juho Rousu and Florence d'Alché-Buc},
journal= {arXiv preprint arXiv:2211.08958},
year = {2022}
}