A convex formulation for high-dimensional sparse sliced inverse regression

Kean Ming Tan, Zhaoran Wang, Tong Zhang, Han Liu, R. D Cook

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)769-782
Number of pages14
JournalBiometrika
Volume105
Issue number4
DOIs
StatePublished - Dec 1 2018

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Sliced Inverse Regression
Convex optimization
Covariates
High-dimensional
multipliers
Formulation
system optimization
Linear Combination
Subspace
Sufficient Dimension Reduction
Method of multipliers
Alternating Direction Method
Minimal Set
Variable Selection
Conditional Distribution
Convex Optimization
Higher Dimensions
Direction compound
Numerical Study
methodology

Keywords

  • Convex optimization
  • Dimension reduction
  • Nonparametric regression
  • Principal fitted component.

Cite this

A convex formulation for high-dimensional sparse sliced inverse regression. / Tan, Kean Ming; Wang, Zhaoran; Zhang, Tong; Liu, Han; Cook, R. D.

In: Biometrika, Vol. 105, No. 4, 01.12.2018, p. 769-782.

Research output: Contribution to journalArticle

Tan, Kean Ming ; Wang, Zhaoran ; Zhang, Tong ; Liu, Han ; Cook, R. D. / A convex formulation for high-dimensional sparse sliced inverse regression. In: Biometrika. 2018 ; Vol. 105, No. 4. pp. 769-782.
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