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Vector-Valued Least-Squares Regression under Output Regularity Assumptions
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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en
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50
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Journal of Machine Learning Research, Volume 23, pp. 1-50
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.
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Brogat-Motte, L, Rudi, A, Brouard, C, Rousu, J & d'Alché-Buc, F 2022, 'Vector-Valued Least-Squares Regression under Output Regularity Assumptions', Journal of Machine Learning Research, vol. 23, 344, pp. 1-50. < https://www.jmlr.org/papers/v23/21-1357.html >