| GSparO {GSparO} | R Documentation |
Group sparse optimization
Description
Group sparse optimization (GSparO) for least squares regression by using the proximal gradient algorithm to solve the L_2,1/2 regularization model.
Usage
GSparO(A, b, Initial, group, MaxIter, sparsity)
Arguments
A |
decoding matrix (matrix of predictors) |
b |
noised signal (response) |
Initial |
an initial point of iteration, recommend to set as a column vector of zeros |
group |
group information, a column vector consisting of the length of each group |
MaxIter |
the maximum number of iterations (a stopping criterion), recommend to set as 200 |
sparsity |
a guess of the group sparsity level (the number of nonzero groups) |
Details
GSparO is group sparse optimization for least squares regression described in [Hu et al(2017)], in which the proximal gradient algorithm is implemented to solve the L_2,1/2 regularization model. GSparO is an iterative algorithm consisting of a gradient step for the least squares regression and a proximal steps for the L_2,1/2 penalty, which is analytically formulated in this function. Also, GSparO can solve sparse variable selection problem in absence of group structure. In particular, setting group in GSparO be a vector of ones, GSparO is reduced to the iterative half thresholding algorithm introduced in [Xu et al (2012)]. Copyright by Dr. Yaohua Hu, College of Mathematics and Statistics, Shenzhen University. Email: mayhhu@szu.edu.cn
Author(s)
Yaohua Hu
References
Y. Hu, C. Li, K. Meng, J. Qin, and X. Yang (2017). Group sparse optimization via L_p,q regularization. Journal of Machine Learning Research, to appear.
Z. Xu, X. Chang, F. Xu, and H. Zhang (2012). L_1/2 regularization: A thresholding representation theory and a fast solver. IEEE Transactions on Neural Networks and Learning Systems.
Examples
m <- 256
n <- 1024
sparsity <- 6
gLen <- 16
MaxIter <- 200
gNo <- 1024/gLen
group <- gLen*matrix(1,gNo,1)
A <- matrix(rnorm(m*n,0,1),m,n)
library(ThreeWay)
A <- orth(t(A))
A <- t(A)
gNo1 <- 1:gNo
ActInd <- sample(gNo1,gNo)
Bs <- matrix(0,n,1)
c <- matrix(rnorm(n,0,1),n,1)
for (i in 1:sparsity){
Bs[((ActInd[i]-1)*gLen+1):(ActInd[i]*gLen)] <- matrix(1,gLen,1)}
c <- Bs*c
sigma <- 1e-3
b <- A%*%c + sigma*matrix(runif(m,min=0,max=1),m,1)
Initial <- matrix(0,n,1)
GSparO(A,b,Initial,group,MaxIter,sparsity)