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Versatile Descent Algorithms for Group Regularization and Variable Selection in Generalized Linear Models.

Nathaniel E Helwig1,2

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Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
|February 28, 2025
PubMed
Summary
This summary is machine-generated.

A new adaptively bounded gradient descent (ABGD) algorithm enhances group elastic net penalized regression. This flexible framework offers stable computation and broad applicability across various response distributions, improving efficiency for penalized regression models.

Keywords:
Elastic NetLassoMCPMultinomial RegressionSCAD

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Area of Science:

  • Statistics
  • Computational Statistics
  • Machine Learning

Background:

  • Group elastic net penalized regression is crucial for high-dimensional data analysis.
  • Existing algorithms often lack flexibility and computational stability.
  • There is a need for methods applicable to diverse response distributions and predictor sets.

Purpose of the Study:

  • To propose a novel adaptively bounded gradient descent (ABGD) algorithm for group elastic net penalized regression.
  • To develop a flexible and computationally stable framework for penalized regression.
  • To extend the applicability of group penalization to a wider range of response distributions.

Main Methods:

  • Development of an adaptively bounded gradient descent (ABGD) algorithm.
  • Adaptive bounding of the Fisher information matrix for computational stability.
  • Implementation in the `grpnet` R package supporting various response distributions (Gaussian, binomial, Poisson, multinomial, negative binomial, gamma, inverse Gaussian).

Main Results:

  • The ABGD algorithm provides a flexible and stable computational framework.
  • The method does not require predictor orthogonalization and is broadly applicable.
  • Simulations and real data show the algorithm is efficient, matching or exceeding existing methods for common distributions and enabling high-dimensional multinomial regression.

Conclusions:

  • The proposed ABGD algorithm offers a significant advancement in penalized regression.
  • Its flexibility and efficiency make it suitable for diverse statistical modeling tasks, including high-dimensional genomic data.
  • The `grpnet` R package provides accessible implementation for researchers.