NDLI: A coordinate descent algorithm for computing penalized smooth quantile regression

Content Provider	Springer Nature Link
Author	Mkhadri, Abdallah Ouhourane, Mohamed Oualkacha, Karim
Copyright Year	2016
Abstract	The computation of penalized quantile regression estimates is often computationally intensive in high dimensions. In this paper we propose a coordinate descent algorithm for computing the penalized smooth quantile regression (cdaSQR) with convex and nonconvex penalties. The cdaSQR approach is based on the approximation of the objective check function, which is not differentiable at zero, by a modified check function which is differentiable at zero. Then, using the maximization-minimization trick of the gcdnet algorithm (Yang and Zou in, J Comput Graph Stat 22(2):396–415, 2013), we update each coefficient simply and efficiently. In our implementation, we consider the convex penalties $$\ell _1+\ell _2$$ and the nonconvex penalties SCAD (or MCP) $$+ \ell _2$$ . We establishe the convergence property of the csdSQR with $$\ell _1+\ell _2$$ penalty. The numerical results show that our implementation is an order of magnitude faster than its competitors. Using simulations we compare the speed of our algorithm to its competitors. Finally, the performance of our algorithm is illustrated on three real data sets from diabetes, leukemia and Bardet–Bidel syndrome gene expression studies.
Starting Page	865
Ending Page	883
Page Count	19
File Format	PDF
ISSN	09603174
Journal	Statistics and Computing
Volume Number	27
Issue Number	4
e-ISSN	15731375
Language	English
Publisher	Springer US
Publisher Date	2016-05-10
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Variable selection Quantile regression Smooth check function Coordinate descent algorithm Statistics and Computing/Statistics Programs Artificial Intelligence (incl. Robotics) Statistical Theory and Methods Probability and Statistics in Computer Science
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Theoretical Computer Science Computational Theory and Mathematics Statistics, Probability and Uncertainty

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