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Hard thresholding regression.

Qiang Sun1, Bai Jiang2, Hongtu Zhu3

  • 1Department of Statistical Sciences, University of Toronto, Toronto, ON, Canada.

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|October 19, 2020
PubMed
Summary
This summary is machine-generated.

We introduce hard thresholding regression (HTR), a novel two-stage convex algorithm for high-dimensional sparse linear regression. HTR effectively estimates sparse models and achieves strong oracle properties, validated by simulations and real data analysis.

Keywords:
Lassobest subset selectionlinear programmingoracle propertysparsityvariable selection

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Area of Science:

  • Statistics
  • Machine Learning
  • Econometrics

Background:

  • High-dimensional data presents challenges for traditional regression.
  • Sparse linear regression models are crucial for identifying relevant predictors.

Purpose of the Study:

  • To propose a novel method, hard thresholding regression (HTR), for estimating high-dimensional sparse linear regression models.
  • To develop a two-stage convex algorithm that approximates ℓ0-penalized regression.

Main Methods:

  • A two-stage convex algorithm is employed.
  • The first stage computes an initial estimator.
  • The second stage refines the estimate by leveraging information from the initial stage.

Main Results:

  • The proposed HTR estimator demonstrates strong oracle properties.
  • The method is robust across a wide range of regularization parameters.
  • Numerical simulations and a real-world data example validate the methodology.

Conclusions:

  • HTR provides an effective approach for high-dimensional sparse linear regression.
  • The two-stage algorithm offers theoretical guarantees and practical performance.
  • The method is well-supported by empirical evidence.