Penalized Quantile Regression for Distributed Big Data Using the Slack Variable Representation

Penalized quantile regression is a widely used tool for analyzing high-dimensional data with heterogeneity. Although its estimation theory has been well studied in the literature, its computation s...

[1]  B. Mercier,et al.  A dual algorithm for the solution of nonlinear variational problems via finite element approximation , 1976 .

[2]  Michael W. Mahoney,et al.  Quantile Regression for Large-Scale Applications , 2013, SIAM J. Sci. Comput..

[3]  Paulo Cortez,et al.  A Proactive Intelligent Decision Support System for Predicting the Popularity of Online News , 2015, EPIA.

[4]  Lei Guan,et al.  An Efficient ADMM-Based Algorithm to Nonconvex Penalized Support Vector Machines , 2018, 2018 IEEE International Conference on Data Mining Workshops (ICDMW).

[5]  Cun-Hui Zhang.  Nearly unbiased variable selection under minimax concave penalty , 2010, 1002.4734.

[6]  Wotao Yin,et al.  Global Convergence of ADMM in Nonconvex Nonsmooth Optimization , 2015, Journal of Scientific Computing.

[7]  Lan Wang,et al.  A Parallel Algorithm for Large-Scale Nonconvex Penalized Quantile Regression , 2017 .

[8]  Jianqing Fan,et al.  ADAPTIVE ROBUST VARIABLE SELECTION. , 2012, Annals of statistics.

[9]  Bo Peng,et al.  An Iterative Coordinate Descent Algorithm for High-Dimensional Nonconvex Penalized Quantile Regression , 2015 .

[10]  Yunzhang Zhu.  An Augmented ADMM Algorithm With Application to the Generalized Lasso Problem , 2017 .

[11]  Shiqian Ma,et al.  ADMM for High-Dimensional Sparse Penalized Quantile Regression , 2018, Technometrics.

[12]  Guang Cheng,et al.  Distributed inference for quantile regression processes , 2017, The Annals of Statistics.

[13]  Liqun Yu,et al.  ADMM for Penalized Quantile Regression in Big Data , 2017 .

[14]  R. Rockafellar,et al.  Prox-regular functions in variational analysis , 1996 .

[15]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[16]  Jianqing Fan,et al.  Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties , 2001 .

[17]  R. Glowinski,et al.  Sur l'approximation, par éléments finis d'ordre un, et la résolution, par pénalisation-dualité d'une classe de problèmes de Dirichlet non linéaires , 1975 .

[18]  Chih-Jen Lin,et al.  Distributed Newton Methods for Regularized Logistic Regression , 2015, PAKDD.

[19]  D. Hunter,et al.  Quantile Regression via an MM Algorithm , 2000 .

[20]  H. Zou.  The Adaptive Lasso and Its Oracle Properties , 2006 .