# Sparse Sliced Inverse Regression Via Lasso

arXiv: https://arxiv.org/abs/1611.06655 · HTML: https://mlsanity.com/paper/1611.06655/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2016.

## Built on by (most cited first, 8 of 8)

- [Semi-Supervised Quantile Estimation: Robust and Efficient Inference in High Dimensional Settings](https://mlsanity.com/paper/2201.10208/) (2022)
- [Nonlinear Sufficient Dimension Reduction with a Stochastic Neural Network](https://mlsanity.com/paper/2210.04349/) (2022)
- [Statistical process monitoring of artificial neural networks](https://mlsanity.com/paper/2209.07436/) (2022)
- [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)
- [An Adaptive Dimension Reduction Estimation Method for High-dimensional Bayesian Optimization](https://mlsanity.com/paper/2403.05425/) (2024)
- [Differentially Private Sliced Inverse Regression: Minimax Optimality and Algorithm](https://mlsanity.com/paper/2401.08150/) (2024)
- [Robust Dual-Regularized Variable Selection under Outlier Contamination](https://mlsanity.com/paper/2609.21342/) (2026)

## Abstract (arXiv)

For multiple index models, it has recently been shown that the sliced inverse regression (SIR) is consistent for estimating the sufficient dimension reduction (SDR) space if and only if ρ=limfracpn=0, where p is the dimension and n is the sample size. Thus, when p is of the same or a higher order of n, additional assumptions such as sparsity must be imposed in order to ensure consistency for SIR. By constructing artificial response variables made up from top eigenvectors of the estimated conditional covariance matrix, we introduce a simple Lasso regression method to obtain an estimate of the SDR space. The resulting algorithm, Lasso-SIR, is shown to be consistent and achieve the optimal convergence rate under certain sparsity conditions when p is of order o(n2λ2), where λ is the generalized signal-to-noise ratio. We also demonstrate the superior performance of Lasso-SIR compared with existing approaches via extensive numerical studies and several real data examples.