Description Usage Arguments Details Value Author(s) References Examples
To perform two methods, Kappa and PASS, for selecting tuning parameters in regularized procedures such as LASSO, SCAD, and adaptive LASSO
1 2 3 4 5 6 |
data |
It is an n by (p+1) matrix, where the first p columns form the design matrix and the last column is response vector. |
base |
It is the base procedure used for variable selection. Three choices of base are "LASSO", "SCAD", and "aLASSO". |
lambda.grid |
It is a vector consisting of the values of tuning parameter lambda to be evaluated. If lambda.grid=NULL, a grid of lambda's will be decided automatically, with specified number of lambda's to be considered. |
num.grid |
It is the number of lambda's to be considered, where a grid of lambda's is decided manually or automatically. The default value is 20. |
num.split |
It is the number of random half-half splittings. The default value is 20. |
alpha |
It is the threshold only used for the Kappa selection method. It is not a tuning parameter. The default value is 0.1. |
x |
This is the output object of class |
... |
Not used. |
Because the data matrix will be centerized so that the column means are zero, there is no need an intercept column in the data matrix.
Function print.lass(x)
prints the two estimated optimal values of tuning parameter lambda and function plot.lass(x)
plots
the two tuning parameter selection processess, where x
is the output of function pass
.
pass.values |
The values evaluated over lambda.grid using the PASS criterion. A curve based on these values can be drawn using function |
kappa.values |
The values evaluated over lambda.grid using the Kappa criterion. A curve based on these values can be drawn using function |
lambda.pass |
The estimated optimal value for the tuning parameter lambda using the PASS criterion |
lambda.kappa |
The estimated optimal value for the tuning parameter lambda using the Kappa criterion (adjusted for the threshold |
beta.pass |
The estimated coefficients using selected lambda by the PASS criterion |
beta.kappa |
The estimated coefficients using selected lambda by the Kappa criterion (adjusted for the threshold |
subset.pass |
The selected submodel by the PASS criterion |
subset.kappa |
The selected submodel by the Kappa criterion (adjusted for the threshold |
Yixin Fang, Wei Sun, Junhui Wang
(1) Sun, Wang, and Fang (2012+) Consistent selection of tuning parameters via variable selection stability. Revision Submmitted. Available at arXiv.
(2) Fang, Wang, and Sun (2012+) A PASS for tuning parameter selection in regularized regression. Submmitted. Available at arXiv.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | library(MASS)
library(lars)
library(ncvreg)
beta=c(3,1.5,0,0,2,0,0,0)
p=8
n=100
sigma=1
rho=0.5
set.seed(100)
x=matrix(0, n, p)
x[,1]<-rnorm(n, 0, 1)
for (i in 2:p) x[,i]<-rho*x[,i-1]+sqrt(1-rho^2)*rnorm(n, 0, 1)
y=x%*%beta+sigma*rnorm(n, 0, 1)
data<-cbind(x,y)
lambda.grid=10^seq(-2,2,length=20)
results<-pass(data=data, base="LASSO", lambda.grid=lambda.grid, num.grid=20, num.split=20)
print(results)
plot(results)
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