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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Majorization Minimization by Coordinate Descent for Concave Penalized Generalized Linear Models.

Dingfeng Jiang1, Jian Huang2

  • 1Exploratory Statistics, Data and Statistical Science, AbbVie Inc. dingfengjiang@gmail.com.

Statistics and Computing
|October 14, 2014
PubMed
Summary

A new Majorization Minimization by Coordinate Descent (MMCD) algorithm efficiently computes concave penalized solutions for high-dimensional generalized linear models. This method improves computational speed for variable selection tasks like penalized logistic regression.

Keywords:
logistic regressionminimax concave penaltyp ≫ n modelssmoothly clipped absolute deviation penaltyvariable selection

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Area of Science:

  • Statistics
  • Machine Learning
  • Computational Statistics

Background:

  • Concave penalties like smoothly clipped absolute deviation (SCAD) and minimax concave penalty (MCP) offer theoretical advantages for variable selection.
  • Computing solutions for concave penalized models, especially in high-dimensional settings, presents significant computational challenges.

Purpose of the Study:

  • To develop an efficient algorithm for computing concave penalized solutions in generalized linear models.
  • To address the computational difficulties associated with variable selection using concave penalties in high-dimensional data.

Main Methods:

  • Propose a novel Majorization Minimization by Coordinate Descent (MMCD) algorithm.
  • The MMCD algorithm majorizes the negative log-likelihood with a quadratic loss without approximating the penalty function.
  • Avoids the need for a scaling factor in each solution update, enhancing computational efficiency.

Main Results:

  • Established theoretical convergence properties for the MMCD algorithm under regularity conditions.
  • Implemented the MMCD algorithm for penalized logistic regression using SCAD and MCP penalties.
  • Demonstrated sufficient speed and effectiveness of MMCD in high-dimensional settings where covariates exceed sample size.

Conclusions:

  • The MMCD algorithm provides an efficient and theoretically sound method for concave penalized variable selection in high-dimensional generalized linear models.
  • MMCD offers a practical solution for computationally intensive tasks in penalized regression, particularly for logistic regression models.
  • The algorithm's efficiency makes it suitable for analyzing complex, high-dimensional datasets in statistical modeling and machine learning.