Abstract: In this talk, I will report some recent developments in Sliced Inverse Regression(SIR). In semi-parametric regression, researchers often assume that response depends on a low dimensional projection of the predictors through an unknown link function, i.e., index models. SIR is proposed to estimate the low dimensional projection matrix under mild conditions and has gained successes in various applications including but not limited to biological, financial data. Because of the high dimensionality of the modern data, efficient variants of SIR for high dimensional data are of particular interest. SIR has been considered to be a supervised counterpart of PCA since its birth and is treated as generalized eigenvector problems in literature. Our recent results indicate that a more appropriate prototype of high dimensional SIR might be the sparse linear regression rather than the sparse PCA.