In this paper, we study the variational problem associated to support vector regression in Banach function spaces. Using the Fenchet-Roclatfellar duality theory, we give an explicit formulation of the dual problem as well as of the related optimality conditions. Moreover, we provide a new computational framework for solving the problem which relies on a tensor-kernel representation. This analysis overcomes the typical difficulties connected to learning in Banach spaces. We finally present a large class of tensor-kernels to which our theory fully applies: power series tensor kernels. This type of kernels describes Banach spaces of analytic functions and includes generalizations of the exponential and polynomial kernels as well as, in the complex case, generalizations of the Szego and Bergman kernels.
Generalized support vector regression: Duality and tensor-kernel representation / Salzo, S; Suykens, Jak. - In: ANALYSIS AND APPLICATIONS. - ISSN 0219-5305. - 18:1(2020), pp. 149-183. [10.1142/S0219530519410069]
Generalized support vector regression: Duality and tensor-kernel representation
Salzo S
;
2020
Abstract
In this paper, we study the variational problem associated to support vector regression in Banach function spaces. Using the Fenchet-Roclatfellar duality theory, we give an explicit formulation of the dual problem as well as of the related optimality conditions. Moreover, we provide a new computational framework for solving the problem which relies on a tensor-kernel representation. This analysis overcomes the typical difficulties connected to learning in Banach spaces. We finally present a large class of tensor-kernels to which our theory fully applies: power series tensor kernels. This type of kernels describes Banach spaces of analytic functions and includes generalizations of the exponential and polynomial kernels as well as, in the complex case, generalizations of the Szego and Bergman kernels.File | Dimensione | Formato | |
---|---|---|---|
Salzo_Generalized-support_2020.pdf
solo gestori archivio
Tipologia:
Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
592.02 kB
Formato
Adobe PDF
|
592.02 kB | Adobe PDF | Contatta l'autore |
Salzo_preprint_Generalized-support_2020.pdf
accesso aperto
Tipologia:
Documento in Pre-print (manoscritto inviato all'editore, precedente alla peer review)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
317.4 kB
Formato
Adobe PDF
|
317.4 kB | Adobe PDF |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.