Data Science Seminar Series: Stéphane Girard

on the December 12, 2019

17:00 to 18:30
The Data Science Seminar Series bring high profile researchers to Université Grenoble Alpes to show the increasing role of data science in modern research. It is open to all researchers of Université Grenoble Alpes. For the 4th seminar of this year, we will welcome Stéphane Girard from Inria Grenoble Rhone-Alpes team Mistis.
Stéphane Girard from Inria Grenoble Rhone-Alpes team Mistis, will give a talk about “An introduction to SIR: A statistical method for dimension reduction in multivariate regression”. The event will take place on Thursday 12 December at IM2AG building. The event will be followed by a coffee break.

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. In this paper, a Gaussian prior distribution is introduced 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 is provided
together with an application to the retrieval of Mars surface physical properties from hyperspectral images.


Related articles

https://hal.inria.fr/inria-00180458
https://hal.inria.fr/inria-00276116

Published on November 21, 2019

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ENSIMAG - Amphi H
Campus universitaire de Grenoble