An introduction to SIR: A statistical method for dimension reduction in multivariate regression

Sliced Inverse Regression (SIR) is an effective method for dimension reduction in high-dimensional regression problems. It 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 possibleand a regularization technique has to be used. 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 asan application to the estimation of Mars surface physical properties from hyperspectral images are provided.