# Optimal Sparse Sliced Inverse Regression via Random Projection

arXiv: https://arxiv.org/abs/2305.05141 · HTML: https://mlsanity.com/paper/2305.05141/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 May 2023.

## Built on by (most cited first, 1 of 1)

- [Random-projection ensemble dimension reduction](https://mlsanity.com/paper/2410.04922/) (2024)

## Abstract (arXiv)

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.