General risk measures for robust machine learning - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Foundations of Data Science Année : 2019

General risk measures for robust machine learning

Mesures de risque générales pour l'apprentissage automatique robuste

Résumé

A wide array of machine learning problems are formulated as the minimization of the expectation of a convex loss function on some parameter space. Since the probability distribution of the data of interest is usually unknown, it is is often estimated from training sets, which may lead to poor out-of-sample performance. In this work, we bring new insights in this problem by using the framework which has been developed in quantitative finance for risk measures. We show that the original min-max problem can be recast as a convex minimization problem under suitable assumptions. We discuss several important examples of robust formulations, in particular by defining ambiguity sets based on $\varphi$-divergences and the Wasserstein metric. We also propose an efficient algorithm for solving the corresponding convex optimization problems involving complex convex constraints. Through simulation examples, we demonstrate that this algorithm scales well on real data sets.
Fichier principal
Vignette du fichier
article.pdf (940.07 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02109418 , version 1 (25-04-2019)

Identifiants

Citer

Emilie Chouzenoux, Henri Gérard, Jean-Christophe Pesquet. General risk measures for robust machine learning. Foundations of Data Science, 2019, 1 (3), pp.249-269. ⟨10.3934/fods.2019011⟩. ⟨hal-02109418⟩
221 Consultations
336 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More