A0461
Title: Optimal sparse sliced inverse regression via random projection
Authors: Jia Zhang - Southwestern University of Finance and Economics (China) [presenting]
Abstract: A novel simple sparse sliced inverse regression method is proposed based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of low-dimensional (generalized) eigenvalue decompositions, which facilitates high computational efficiency. Theoretically, it is proven that this method achieves the minimax optimal rate of convergence under suitable assumptions. Furthermore, the algorithm involves a delicate reweighting scheme, which can significantly enhance the identifiability of the active set of covariates. Extensive numerical experiments demonstrate the high superiority of the proposed algorithm in comparison to competing methods.
