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Sparse Sliced Inverse Regression Via Lasso.

Qian Lin1,2,3, Zhigen Zhao1,2,3, Jun S Liu1,2,3

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|September 21, 2020
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A new Lasso-SIR method estimates the sufficient dimension reduction (SDR) space consistently, even when data dimensions exceed sample size. This approach offers optimal convergence rates under sparsity conditions.

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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.