rk_tune {kko}

tune random feature number for KKO.

Description

The function applys KKO with different random feature numbers to tune the optimal number.

Usage

rk_tune(
  X,
  y,
  X_k,
  rfn_range,
  n_stb,
  cv_folds,
  frac_stb = 1/2,
  nCores_para = 1,
  rkernel = "laplacian",
  rk_scale = 1
)

Arguments

X

design matrix of additive model; rows are observations and columns are variables.

y

response of addtive model.

X_k

knockoffs matrix of design; the same size as X.

rfn_range

a vector of random feature expansion numbers to be tuned.

n_stb

number of subsampling in KKO.

cv_folds

the folds of cross-validation for tuning group lasso.

frac_stb

fraction of subsample.

nCores_para

number of cores for parallelizing subsampling.

rkernel

kernel choices. Default is "laplacian". Other choices are "cauchy" and "gaussian".

rk_scale

scaling parameter of sampling distribution for random feature expansion. For gaussian kernel, it is standard deviation of gaussian sampling distribution.

Value

a list of tuning results.

rfn_tune	tuned optimal random feature number.
rfn_range	a vector of random feature expansion numbers to be tuned.
scores	scores of random feature numbers. rfn_tune has the maximal score.
Pi_list	a list of subsample selection results for each random feature number.

Author(s)

Xiaowu Dai, Xiang Lyu, Lexin Li

Examples

library(knockoff)
p=5 # number of predictors
sig_mag=100 # signal strength
n= 100 # sample size
rkernel="laplacian" # kernel choice
s=2  # sparsity, number of nonzero component functions
rk_scale=1  # scaling paramtere of kernel
rfn_range= c(2,3,4)  # number of random features
cv_folds=15  # folds of cross-validation in group lasso
n_stb=10 # number of subsampling
frac_stb=1/2 # fraction of subsample
nCores_para=2 # number of cores for parallelization
X=matrix(rnorm(n*p),n,p)%*%chol(toeplitz(0.3^(0:(p-1))))   # generate design
X_k = create.second_order(X) # generate knockoff
reg_coef=c(rep(1,s),rep(0,p-s))  # regression coefficient
reg_coef=reg_coef*(2*(rnorm(p)>0)-1)*sig_mag
y=X%*% reg_coef + rnorm(n) # response

rk_tune(X,y,X_k,rfn_range,n_stb,cv_folds,frac_stb,nCores_para,rkernel,rk_scale)