Sparse Sliced Inverse Regression Via Lasso

Area of Science:

• Statistics
• Machine Learning
• Dimensionality Reduction

Background:

• Sliced inverse regression (SIR) consistency for sufficient dimension reduction (SDR) estimation requires p << n.
• High-dimensional data (p >= n) necessitates additional assumptions like sparsity for SIR consistency.

Purpose of the Study:

• To develop a consistent SDR estimation method for high-dimensional data.
• To introduce a novel algorithm, Lasso-SIR, that addresses the limitations of traditional SIR.

Main Methods:

• Constructing artificial response variables from eigenvectors of the conditional covariance matrix.
• Applying Lasso regression to estimate the SDR space using these artificial responses.

Main Results:

• Lasso-SIR achieves consistency and optimal convergence rates under sparsity.
• Performance is validated through simulations and real-world data analysis, outperforming existing methods.

Conclusions:

• Lasso-SIR provides a robust solution for SDR estimation in high-dimensional settings.
• The method enhances the applicability of SDR techniques when dimensionality is a challenge.