cv.iss {Libra}

CV for ISS

Description

Cross-validation method to tuning the parameter t for ISS.

Usage

cv.iss(
  X,
  y,
  K = 5,
  t,
  intercept = TRUE,
  normalize = TRUE,
  plot.it = TRUE,
  se = TRUE,
  ...
)

Arguments

X

An n-by-p matrix of predictors

y

Response Variable

K

Folds number for CV. Default is 5.

t

A vector of predecided tuning parameter.

intercept

If TRUE, an intercept is included in the model (and not penalized), otherwise no intercept is included. Default is TRUE.

normalize

if TRUE, each variable is scaled to have L2 norm square-root n. Default is TRUE.

plot.it

Plot it? Default is TRUE

se

Include standard error bands? Default is TRUE

...

Additonal arguments passing to lb

Details

K-fold cross-validation method is used to tuning the parameter $t$ for ISS. Mean square error is used as prediction error.

Value

A list is returned. The list contains a vector of parameter t, crossvalidation error cv.error, and the estimated standard deviation for it cv.sd

Author(s)

Feng Ruan, Jiechao Xiong and Yuan Yao

References

Ohser, Ruan, Xiong, Yao and Yin, Sparse Recovery via Differential Inclusions, https://arxiv.org/abs/1406.7728

Examples

#Examples in the reference paper
library(MASS)
n = 200;p = 100;k = 30;sigma = 1
Sigma = 1/(3*p)*matrix(rep(1,p^2),p,p)
diag(Sigma) = 1
A = mvrnorm(n, rep(0, p), Sigma)
u_ref = rep(0,p)
supp_ref = 1:k
u_ref[supp_ref] = rnorm(k)
u_ref[supp_ref] = u_ref[supp_ref]+sign(u_ref[supp_ref])
b = as.vector(A%*%u_ref + sigma*rnorm(n))
cv.iss(A,b,intercept = FALSE,normalize = FALSE)