1.2 On the regularization of Sliced Inverse Regression (Stéphane Girard)

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Par Universite Paris 1 Pantheon-Sorbonne, découvert par Player FM et notre communauté - Le copyright est détenu par l'éditeur, non par Player F, et l'audio est diffusé directement depuis ses serveurs. Appuyiez sur le bouton S'Abonner pour suivre les mises à jour sur Player FM, ou collez l'URL du flux dans d'autre applications de podcasts.
Sliced Inverse Regression (SIR) is an effective method for dimension reduction in highdimensional 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 an interpretation of SIR axes as solutions of an inverse regression problem. A prior distribution is then 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, and compared on simulated data. An application to the estimation of Mars surface physical properties from hyperspectral images is provided.

12 episodes