Skip to Main content Skip to Navigation
Documents associated with scientific events

Regularization methods for Sliced Inverse Regression

Caroline Bernard-Michel 1 Laurent Gardes 1 Stéphane Girard 1 
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
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.
Document type :
Documents associated with scientific events
Complete list of metadata

Cited literature [9 references]  Display  Hide  Download
Contributor : Stephane Girard Connect in order to contact the contributor
Submitted on : Wednesday, April 30, 2014 - 2:55:40 PM
Last modification on : Thursday, January 20, 2022 - 5:30:18 PM
Long-term archiving on: : Wednesday, July 30, 2014 - 1:25:30 PM


Files produced by the author(s)


  • HAL Id : hal-00985822, version 1



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



Record views


Files downloads