Sparse Multiple Kernel Learning: Support Identification via Mirror Stratifiability - Archive ouverte HAL
Communication Dans Un Congrès Année : 2018

Sparse Multiple Kernel Learning: Support Identification via Mirror Stratifiability

Lorenzo Rosasco
  • Fonction : Auteur
Silvia Villa
  • Fonction : Auteur

Résumé

In statistical machine learning, kernel methods allow to consider infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done by solving an optimization problem depending on a data fit term and a suitable regularizer. In this paper we consider feature maps which are the concatenation of a fixed, possibly large, set of simpler feature maps. The penalty is a sparsity inducing one, promoting solutions depending only on a small subset of the features. The group lasso problem is a special case of this more general setting. We show that one of the most popular optimization algorithms to solve the regularized objective function, the forward-backward splitting method, allows to perform feature selection in a stable manner. In particular, we prove that the set of relevant features is identified by the algorithm after a finite number of iterations if a suitable qualification condition holds. Our analysis rely on the notions of stratification and mirror stratifiability.
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Dates et versions

hal-03886322 , version 1 (06-12-2022)

Identifiants

Citer

Guillaume Garrigos, Lorenzo Rosasco, Silvia Villa. Sparse Multiple Kernel Learning: Support Identification via Mirror Stratifiability. 2018 26th European Signal Processing Conference (EUSIPCO), Sep 2018, Rome, Italy. pp.1077-1081, ⟨10.23919/EUSIPCO.2018.8553267⟩. ⟨hal-03886322⟩
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