Vector-Valued Least-Squares Regression Under Output Regularity Assumptions
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
Text
Brogat-Motte et al. "Vector-Valued Least-Squares Regression Under Output Regularity Assumptions." Journal of Machine Learning Research, 2022.Markdown
[Brogat-Motte et al. "Vector-Valued Least-Squares Regression Under Output Regularity Assumptions." Journal of Machine Learning Research, 2022.](https://mlanthology.org/jmlr/2022/brogatmotte2022jmlr-vectorvalued/)BibTeX
@article{brogatmotte2022jmlr-vectorvalued,
title = {{Vector-Valued Least-Squares Regression Under Output Regularity Assumptions}},
author = {Brogat-Motte, Luc and Rudi, Alessandro and Brouard, Céline and Rousu, Juho and d'Alché-Buc, Florence},
journal = {Journal of Machine Learning Research},
year = {2022},
pages = {1-50},
volume = {23},
url = {https://mlanthology.org/jmlr/2022/brogatmotte2022jmlr-vectorvalued/}
}