Optimal Sparse Sliced Inverse Regression via Random Projection

Jia Zhang; Runxiong Wu; Xin Chen

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arXiv · 2305.05141

Optimal Sparse Sliced Inverse Regression via Random Projection

Jia Zhang·Runxiong Wu·Xin Chen

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Abstract

We propose a novel sparse sliced inverse regression method 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, we prove that this method achieves the minimax optimal rate of convergence under suitable assumptions. Furthermore, our algorithm involves a delicate reweighting scheme, which can significantly enhance the identifiability of the active set of covariates. Extensive numerical studies demonstrate high superiority of the proposed algorithm in comparison to competing methods.

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Jia Zhang, Runxiong Wu, Xin Chen. 2023-05-09. Optimal Sparse Sliced Inverse Regression via Random Projection. https://arxiv.org/abs/2305.05141

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