LPNN‐based approach for LASSO problem via a sequence of regularized minimizations

2021 ◽  
Author(s):  
Anis Zeglaoui ◽  
Anouar Houmia ◽  
Maher Mejai ◽  
Radhouane Aloui
Keyword(s):  
Lasso Problem

scholarly journals Method for Solving LASSO Problem Based on Multidimensional Weight

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Chen ChunRong ◽  
Chen ShanXiong ◽  
Chen Lin ◽  
Zhu YuChen
Keyword(s):  
Stepwise Regression ◽  
Principal Component ◽  
Threshold Value ◽  
Information Criteria ◽  
Pima Indians ◽  
Least Angle Regression ◽  
Lasso Problem ◽  
Selection Operator ◽  
Excellent Property ◽  
The Impact

In the data mining, the analysis of high-dimensional data is a critical but thorny research topic. The LASSO (least absolute shrinkage and selection operator) algorithm avoids the limitations, which generally employ stepwise regression with information criteria to choose the optimal model, existing in traditional methods. The improved-LARS (Least Angle Regression) algorithm solves the LASSO effectively. This paper presents an improved-LARS algorithm, which is constructed on the basis of multidimensional weight and intends to solve the problems in LASSO. Specifically, in order to distinguish the impact of each variable in the regression, we have separately introduced part of principal component analysis (Part_PCA), Independent Weight evaluation, and CRITIC, into our proposal. We have explored that these methods supported by our proposal change the regression track by weighted every individual, to optimize the approach direction, as well as the approach variable selection. As a consequence, our proposed algorithm can yield better results in the promise direction. Furthermore, we have illustrated the excellent property of LARS algorithm based on multidimensional weight by the Pima Indians Diabetes. The experiment results show an attractive performance improvement resulting from the proposed method, compared with the improved-LARS, when they are subjected to the same threshold value.

scholarly journals Bounded Perturbation Resilience of Two Modified Relaxed CQ Algorithms for the Multiple-Sets Split Feasibility Problem

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 197
Author(s):  
Yingying Li ◽  
Yaxuan Zhang
Keyword(s):  
Hilbert Spaces ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Step Size ◽  
Bounded Perturbation ◽  
Bounded Perturbation Resilience ◽  
Perturbation Resilience ◽  
Lasso Problem ◽  
Bounded Perturbations ◽  
Split Feasibility

In this paper, we present some modified relaxed CQ algorithms with different kinds of step size and perturbation to solve the Multiple-sets Split Feasibility Problem (MSSFP). Under mild assumptions, we establish weak convergence and prove the bounded perturbation resilience of the proposed algorithms in Hilbert spaces. Treating appropriate inertial terms as bounded perturbations, we construct the inertial acceleration versions of the corresponding algorithms. Finally, for the LASSO problem and three experimental examples, numerical computations are given to demonstrate the efficiency of the proposed algorithms and the validity of the inertial perturbation.

scholarly journals Local Linear Convergence of ISTA and FISTA on the LASSO Problem

2016 ◽  
Vol 26 (1) ◽  
pp. 313-336 ◽  
Author(s):  
Shaozhe Tao ◽  
Daniel Boley ◽  
Shuzhong Zhang
Keyword(s):  
Linear Convergence ◽  
Local Linear Convergence ◽  
Local Linear ◽  
Lasso Problem

scholarly journals An inertial parallel algorithm for a finite family of $ G $-nonexpansive mappings applied to signal recovery

2022 ◽  
Vol 7 (2) ◽  
pp. 1775-1790
Author(s):  
Nipa Jun-on ◽  
◽  
Raweerote Suparatulatorn ◽  
Mohamed Gamal ◽  
Watcharaporn Cholamjiak ◽  
...  
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Numerical Experiments ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Signal Recovery ◽  
Numerical Examples ◽  
Different Types ◽  
Lasso Problem ◽  
Inertial Technique

<abstract><p>This study investigates the weak convergence of the sequences generated by the inertial technique combining the parallel monotone hybrid method for finding a common fixed point of a finite family of $ G $-nonexpansive mappings under suitable conditions in Hilbert spaces endowed with graphs. Some numerical examples are also presented, providing applications to signal recovery under situations without knowing the type of noises. Besides, numerical experiments of the proposed algorithms, defined by different types of blurred matrices and noises on the algorithm, are able to show the efficiency and the implementation for LASSO problem in signal recovery.</p></abstract>

scholarly journals Efficient Sparse Semismooth Newton Methods for the Clustered Lasso Problem

2019 ◽  
Vol 29 (3) ◽  
pp. 2026-2052 ◽  
Author(s):  
Meixia Lin ◽  
Yong-Jin Liu ◽  
Defeng Sun ◽  
Kim-Chuan Toh
Keyword(s):  
Newton Methods ◽  
Semismooth Newton ◽  
Semismooth Newton Methods ◽  
Lasso Problem

scholarly journals On Solving Lq-Penalized Regressions

2007 ◽  
Vol 2007 ◽  
pp. 1-13 ◽  
Author(s):  
Tracy Zhou Wu ◽  
Yingyi Chu ◽  
Yan Yu
Keyword(s):  
Solution Method ◽  
Penalized Regression ◽  
Statistical Modelling ◽  
Regression Problem ◽  
Penalized Spline ◽  
Numerical Studies ◽  
Space Transformation ◽  
Lasso Problem ◽  
Computational Difficulty ◽  
Penalized Spline Smoothing

Lq-penalized regression arises in multidimensional statistical modelling where all or part of the regression coefficients are penalized to achieve both accuracy and parsimony of statistical models. There is often substantial computational difficulty except for the quadratic penalty case. The difficulty is partly due to the nonsmoothness of the objective function inherited from the use of the absolute value. We propose a new solution method for the general Lq-penalized regression problem based on space transformation and thus efficient optimization algorithms. The new method has immediate applications in statistics, notably in penalized spline smoothing problems. In particular, the LASSO problem is shown to be polynomial time solvable. Numerical studies show promise of our approach.

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