Regularization methods for Sliced Inverse Regression

Caroline Bernard-Michel 1 Laurent Gardes 1 Stephane Girard 1
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : Sliced Inverse Regression (SIR) is an effective method for dimension reduction in high-dimensional regression problems. The original method, however, requires the inversion of the predictors covariance matrix. In case of collinearity between these predictors or small sample sizes compared to the dimension, the inversion is not possible and a regularization technique has to be used. Our approach is based on a Fisher Lecture given by R.D. Cook where it is shown that SIR axes can be interpreted as solutions of an inverse regression problem. We propose to introduce a Gaussian prior distribution on the unknown parameters of the inverse regression problem in order to regularize their estimation. We show that some existing SIR regularizations can enter our framework, which permits a global understanding of these methods. Three new priors are proposed leading to new regularizations of the SIR method. A comparison on simulated data as well as an application to the estimation of Mars surface physical properties from hyperspectral images are provided.
Type de document :
Documents associés à des manifestations scientifiques -- Hal-inria+
8th International Conference on Operations Research,, Feb 2008, La Havane, Cuba
Liste complète des métadonnées

Littérature citée [9 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-00985822
Contributeur : Stephane Girard <>
Soumis le : mercredi 30 avril 2014 - 14:55:40
Dernière modification le : mercredi 11 avril 2018 - 01:59:46
Document(s) archivé(s) le : mercredi 30 juillet 2014 - 13:25:30

Fichier

slidesCuba.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00985822, version 1

Citation

Caroline Bernard-Michel, Laurent Gardes, Stephane Girard. Regularization methods for Sliced Inverse Regression. 8th International Conference on Operations Research,, Feb 2008, La Havane, Cuba. 〈hal-00985822〉

Partager

Métriques

Consultations de la notice

362

Téléchargements de fichiers

127