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Vector-Valued Least-Squares Regression under Output Regularity Assumptions. (arXiv:2211.08958v1 [stat.ML])
Nov. 17, 2022, 2:11 a.m. | Luc Brogat-Motte, Alessandro Rudi, Céline Brouard, Juho Rousu, Florence d'Alché-Buc
cs.LG updates on arXiv.org arxiv.org
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 …
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