Smoothing ADMM for Sparse-Penalized Quantile Regression with Non-Convex Penalties
Loading...
Access rights
openAccess
publishedVersion
URL
Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
This publication is imported from Aalto University research portal.
View publication in the Research portal (opens in new window)
View/Open full text file from the Research portal (opens in new window)
Other link related to publication (opens in new window)
View publication in the Research portal (opens in new window)
View/Open full text file from the Research portal (opens in new window)
Other link related to publication (opens in new window)
Date
2024
Major/Subject
Mcode
Degree programme
Language
en
Pages
16
Series
IEEE Open journal of Signal Processing, Volume 5, pp. 213-228
Abstract
This paper investigates quantile regression in the presence of non-convex and non-smooth sparse penalties, such as the minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD). The non-smooth and non-convex nature of these problems often leads to convergence difficulties for many algorithms. While iterative techniques such as coordinate descent and local linear approximation can facilitate convergence, the process is often slow. This sluggish pace is primarily due to the need to run these approximation techniques until full convergence at each step, a requirement we term as a secondary convergence iteration. To accelerate the convergence speed, we employ the alternating direction method of multipliers (ADMM) and introduce a novel single-loop smoothing ADMM algorithm with an increasing penalty parameter, named SIAD, specifically tailored for sparse-penalized quantile regression. We first delve into the convergence properties of the proposed SIAD algorithm and establish the necessary conditions for convergence. Theoretically, we confirm a convergence rate of ok14 for the sub-gradient bound of the augmented Lagrangian, where k denotes the number of iterations. Subsequently, we provide numerical results to showcase the effectiveness of the SIAD algorithm. Our findings highlight that the SIAD method outperforms existing approaches, providing a faster and more stable solution for sparse-penalized quantile regression.Description
Funding Information: This work was supported by the Research Council of Norway Publisher Copyright: Authors
Keywords
ADMM, Convergence, Convex functions, non-smooth and non-convex penalties, Optimization, Prediction algorithms, Quantile regression, Signal processing, Signal processing algorithms, Smoothing methods, sparse learning
Other note
Citation
Mirzaeifard, R, Venkategowda, N K D, Gogineni, V C & Werner, S 2024, ' Smoothing ADMM for Sparse-Penalized Quantile Regression with Non-Convex Penalties ', IEEE Open journal of Signal Processing, vol. 5, pp. 213-228 . https://doi.org/10.1109/OJSP.2023.3344395