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 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.

Citation

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 >

Permanent link to this item

https://urn.fi/URN:NBN:fi:aalto-202212146909

Collections

[article-cris] Perustieteiden korkeakoulu / SCI

Show all metadata