Fused Lasso penalized least absolute deviation estimator for high dimensional linear regression

DOI10.3934/naco.2018006zbMath1461.62021OpenAlexW2789724145MaRDI QIDQ1713210

Xianchao Xiu, Yanqing Liu, Huan Zhang, Jiyuan Tao, Lingchen Kong

Publication date: 24 January 2019

Published in: Numerical Algebra, Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/naco.2018006

zbMATH Keywords

least absolute deviationhigh dimensional linear regressionfused Lassolinearized alternating direction method of multipliers

Mathematics Subject Classification ID

Computational methods for problems pertaining to statistics (62-08) Ridge regression; shrinkage estimators (Lasso) (62J07)

Related Items

Automatic variable selection in a linear model on massive data ⋮ An extended linearized alternating direction method of multipliers for fused-Lasso penalized linear regression ⋮ Detection of similar successive groups in a model with diverging number of variable groups ⋮ Homotopy method for matrix rank minimization based on the matrix hard thresholding method

Uses Software

• CVX
• CMARS
• SLEP

Cites Work

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• Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
• CMARS: a new contribution to nonparametric regression with multivariate adaptive regression splines supported by continuous optimization
• The \(L_1\) penalized LAD estimator for high dimensional linear regression
• Statistics for high-dimensional data. Methods, theory and applications.
• A unified primal-dual algorithm framework based on Bregman iteration
• Properties and refinements of the fused Lasso
• Model selection in multivariate adaptive regression splines (MARS) using information complexity as the fitness function
• Stability analysis for stochastic differential equations with infinite Markovian switchings
• Multivariate adaptive regression splines
• Linearized alternating direction method of multipliers for sparse group and fused Lasso models
• A convex version of multivariate adaptive regression splines
• Strong convergence of extragradient method for generalized variational inequalities in Hilbert space
• On the global and linear convergence of the generalized alternating direction method of multipliers
• Pathwise coordinate optimization
• Coordinate descent algorithms for lasso penalized regression
• An augmented Lagrangian based parallel splitting method for separable convex minimization with applications to image processing
• SCAD-Penalized Least Absolute Deviation Regression in High-Dimensional Models
• Decoding by Linear Programming
• Spatial smoothing and hot spot detection for CGH data using the fused lasso
• Shifting Inequality and Recovery of Sparse Signals
• Sparsity and Smoothness Via the Fused Lasso
• The Linearized Alternating Direction Method of Multipliers for Dantzig Selector
• Linearized augmented Lagrangian and alternating direction methods for nuclear norm minimization
• Alternating Direction Methods for Latent Variable Gaussian Graphical Model Selection
• Variable Selection and Model Building via Likelihood Basis Pursuit