Vector-Valued Least-Squares Regression under Output Regularity Assumptions

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 interes...

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Bibliographic Details
Published in:arXiv.org 2022-11
Main Authors: Brogat-Motte, Luc, Alessandro Rudi, Brouard, Céline, Rousu, Juho, d'Alché-Buc, Florence
Format: Article
Language:English
Subjects:
Image classification
Image reconstruction
Least squares method
Metabolites
Regression
Regularity
Statistical analysis
Online Access:Get full text
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Summary: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.
ISSN:2331-8422