# A convex formulation for high-dimensional sparse sliced inverse regression

arXiv: https://arxiv.org/abs/1809.06024 · HTML: https://mlsanity.com/paper/1809.06024/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2018.

## Built on by (most cited first, 5 of 5)

- [Federated Sufficient Dimension Reduction Through High-Dimensional Sparse Sliced Inverse Regression](https://mlsanity.com/paper/2301.09500/) (2023)
- [Differentially private sliced inverse regression in the federated paradigm](https://mlsanity.com/paper/2306.06324/) (2023)
- [Nonlinear Sparse Generalized Canonical Correlation Analysis for Multi-view High-dimensional Data](https://mlsanity.com/paper/2502.18756/) (2025)
- [Nonlinear Multiple Response Regression and Learning of Latent Spaces](https://mlsanity.com/paper/2503.21608/) (2025)
- [Locally Near Optimal Piecewise Linear Regression in High Dimensions via Difference of Max-Affine Functions](https://mlsanity.com/paper/2605.06959/) (2026)

## Abstract (arXiv)

Sliced inverse regression is a popular tool for sufficient dimension reduction, which replaces covariates with a minimal set of their linear combinations without loss of information on the conditional distribution of the response given the covariates. The estimated linear combinations include all covariates, making results difficult to interpret and perhaps unnecessarily variable, particularly when the number of covariates is large. In this paper, we propose a convex formulation for fitting sparse sliced inverse regression in high dimensions. Our proposal estimates the subspace of the linear combinations of the covariates directly and performs variable selection simultaneously. We solve the resulting convex optimization problem via the linearized alternating direction methods of multiplier algorithm, and establish an upper bound on the subspace distance between the estimated and the true subspaces. Through numerical studies, we show that our proposal is able to identify the correct covariates in the high-dimensional setting.