Smoothing ADMM for Sparse-Penalized Quantile Regression with Non-Convex Penalties

Reza Mirzaeifard, Naveen K.D. Venkategowda, Vinay Chakravarthi Gogineni, Stefan Werner

Tutkimustuotos: LehtiartikkeliArticleScientificvertaisarvioitu

27 Lataukset (Pure)

Abstrakti

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 <italic>secondary convergence iteration</italic>. 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 <inline-formula><tex-math notation="LaTeX">$o({k^{-\frac{1}{4}}})$</tex-math></inline-formula> for the sub-gradient bound of the augmented Lagrangian, where <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> 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.

AlkuperäiskieliEnglanti
Sivut213-228
Sivumäärä16
JulkaisuIEEE Open journal of Signal Processing
Vuosikerta5
DOI - pysyväislinkit
TilaJulkaistu - 29 jouluk. 2023
OKM-julkaisutyyppiA1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

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