Robust Phase Retrieval with Non-Convex Penalties

Mirzaeifard, Reza; Venkategowda, Naveen K. D.; Werner, Stefan

doi:10.1109/ieeeconf56349.2022.10052074

Cited by 3 publications

(4 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In light of the proven effectiveness of the ADMM algorithm, its application to quantile regression is appealing. However, implementing ADMM in non-convex scenarios with proven convergence remains challenging since existing non-convex ADMM methods frequently demand either a smooth part or an implicit Lipschitz condition to assure convergence [23,24,31]- [33]. Characteristics like Lipschitz differentiability can be beneficial in regulating the change in the dual update variable in non-convex optimization problems [23].…”

Section: Introductionmentioning

confidence: 99%

“…In scenarios lacking convexity in the objective function, managing the change in the dual update step relative to the primal variables becomes essential for ensuring convergence. Precisely, setting bounds on the change in the dual update step, in accordance with the primal variables, could offer a means for parameter tuning and proof of convergence [23,33]. However, in nonsmooth and non-convex settings, such as sparse penalized quantile regression, the conditions for Lipschitz differentiability or implicit Lipschitz differentiability might not always be satisfied [34].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Mirzaeifard,

Venkategowda,

Gogineni

et al. 2024

IEEE Open J. Signal Process.

Self Cite

View full text Add to dashboard Cite

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 o k − 1 4 for the subgradient 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.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Mirzaeifard,

Venkategowda,

Gogineni

et al. 2024

IEEE Open J. Signal Process.

Self Cite

View full text Add to dashboard Cite

show abstract

“…One solution to this problem is using sparse penalties, such as the minimax concave penalty (MCP) [13] and the smoothly clipped absolute deviation (SCAD) [14], that are capable of intelligently distinguishing between active and inactive coefficients. Although these penalties encourage sparse solutions, they mitigate the bias effect of the l 1 -penalty [15], [16].…”

Section: Introductionmentioning

confidence: 99%

Distributed Quantile Regression with Non-Convex Sparse Penalties

Mirzaeifard,

Gogineni,

Venkategowda

et al. 2023

2023 IEEE Statistical Signal Processing Workshop (SSP)

Self Cite

View full text Add to dashboard Cite

The surge in data generated by IoT sensors has increased the need for scalable and efficient data analysis methods, particularly for robust algorithms like quantile regression, which can be tailored to meet a variety of situations, including nonlinear relationships, distributions with heavy tails, and outliers. This paper presents a sub-gradient-based algorithm for distributed quantile regression with non-convex, and non-smooth sparse penalties such as the Minimax Concave Penalty (MCP) and Smoothly Clipped Absolute Deviation (SCAD). These penalties selectively shrink non-active coefficients towards zero, addressing the limitations of traditional penalties like the l1-penalty in sparse models. Existing quantile regression algorithms with nonconvex penalties are designed for centralized cases, whereas our proposed method can be applied to distributed quantile regression using non-convex penalties, thereby improving estimation accuracy. We provide a convergence proof for our proposed algorithm and demonstrate through numerical simulations that it outperforms state-of-the-art algorithms in sparse and moderately sparse scenarios.

show abstract

“…In light of the proven effectiveness of the ADMM algorithm, its application to quantile regression is quite appealing. However, implementing ADMM in non-convex scenarios with proven convergence remains challenging since existing nonconvex ADMM methods frequently demand either a smooth part or an implicit Lipschitz condition to assure convergence [23,24,31]- [33]. Characteristics like Lipschitz differentiability can be beneficial in regulating the change in the dual update variable in non-convex optimization problems [23].…”

Section: Introductionmentioning

confidence: 99%

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

Mirzaeifard

Venkategowda

Gogineni

et al. 2022

2022 30th European Signal Processing Conference (EUSIPCO)

View full text Add to dashboard Cite

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 like 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 o k − 1 4 for the sub-gradient bound of augmented Lagrangian. 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.

show abstract

Robust Phase Retrieval with Non-Convex Penalties

Cited by 3 publications

References 31 publications

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

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

Distributed Quantile Regression with Non-Convex Sparse Penalties

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

Contact Info

Product

Resources

About