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Preprints, Working Papers, ... Year : 2023

A Review on the Adaptive-Ridge Algorithm with several extensions

Rémy Abergel
Olivier Bouaziz

Abstract

The Adaptive Ridge Algorithm is an iterative algorithm designed for variable selection. It is also known under the denomination of Iteratively Reweighted Least-Squares Algorithm in the communities of Compressed Sensing and Sparse Signals Recovery. Besides, it can also be interpreted as an optimization algorithm dedicated to the minimization of possibly nonconvex q penalized energies (with 0 < q < 2). In the literature, this algorithm can be derived using various mathematical approaches, namely Half Quadratic Minimization, Majorization-Minimization, Alternating Minimization or Local Approximations. In this work, we will show how the Adaptive Ridge Algorithm can be simply derived and analyzed from a single equation, corresponding to a variational reformulation of the q penalty. We will describe in detail how the Adaptive Ridge Algorithm can be numerically implemented and we will perform a thorough experimental study of its parameters. We will also show how the variational formulation of the q penalty combined with modern duality principles can be used to design an interesting variant of the Adaptive Ridge Algorithm dedicated to the minimization of quadratic functions over (nonconvex) q balls.
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Year Month Jours
Avant la publication
Thursday, November 7, 2024
Embargoed file
Thursday, November 7, 2024
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Dates and versions

hal-04051929 , version 1 (30-03-2023)
hal-04051929 , version 2 (19-05-2024)

Identifiers

  • HAL Id : hal-04051929 , version 2

Cite

Rémy Abergel, Olivier Bouaziz, Grégory Nuel. A Review on the Adaptive-Ridge Algorithm with several extensions. 2024. ⟨hal-04051929v2⟩
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