| Title: | Kernel Knockoffs Selection for Nonparametric Additive Models |
| Version: | 1.0.1 |
| Description: | A variable selection procedure, dubbed KKO, for nonparametric additive model with finite-sample false discovery rate control guarantee. The method integrates three key components: knockoffs, subsampling for stability, and random feature mapping for nonparametric function approximation. For more information, see the accompanying paper: Dai, X., Lyu, X., & Li, L. (2021). “Kernel Knockoffs Selection for Nonparametric Additive Models”. arXiv preprint <doi:10.48550/arXiv.2105.11659>. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Depends: | R (≥ 3.6.3) |
| Imports: | grpreg, knockoff, doParallel, parallel, foreach, ExtDist |
| Suggests: | knitr, rmarkdown, ggplot2 |
| Encoding: | UTF-8 |
| LazyData: | false |
| RoxygenNote: | 7.1.2 |
| VignetteBuilder: | knitr |
| Author: | Xiaowu Dai [aut], Xiang Lyu [aut, cre], Lexin Li [aut] |
| Maintainer: | Xiang Lyu <xianglyu@berkeley.edu> |
| NeedsCompilation: | no |
| Packaged: | 2022-01-31 03:32:30 UTC; xianglyu |
| Repository: | CRAN |
| Date/Publication: | 2022-02-01 09:10:05 UTC |
evaluate performance of KKO selection
Description
The function computes {FDP, FPR, TPR} of selection by knockoff filtering on importance scores of KKO.
Usage
KO_evaluation(W, reg_coef, fdr_range = 0.2, offset = 1)
Arguments
W |
importance scores of variables. |
reg_coef |
true regression coefficient. |
fdr_range |
FDR control levels of knockoff filter. |
offset |
0/1. If 1, knockoff+ filter. Otherwise, knockoff filter. |
Value
FDP, FPR, TPR of knockoff filtering at fdr_range.
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 for importance scores
n_stb_tune=5 # number of subsampling for tuning random feature number
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
kko_fit=kko(X,y,X_k,rfn_range,n_stb_tune,n_stb,cv_folds,frac_stb,nCores_para,rkernel,rk_scale)
W=kko_fit$importance_score
fdr_range=c(0.2,0.3,0.4,0.5)
KO_evaluation(W,reg_coef,fdr_range,offset=1)
generate response from nonparametric additive model
Description
The function generate response from additive models of various components.
Usage
generate_data(X, reg_coef, model = "linear", err_sd = 1)
Arguments
X |
design matrix of additive model; rows are observations and columns are variables. | |||||||||||
reg_coef |
regression coefficient vector. | |||||||||||
model |
types of components. Default is "linear". Other choices are
| |||||||||||
err_sd |
standard deviation of regression error. |
Value
reponse vector
Author(s)
Xiaowu Dai, Xiang Lyu, Lexin Li
Examples
p=5 # number of predictors
s=2 # sparsity, number of nonzero component functions
sig_mag=100 # signal strength
n= 200 # sample size
model="poly" # component function type
X=matrix(rnorm(n*p),n,p) %*%chol(toeplitz(0.3^(0:(p-1)))) # generate design
reg_coef=c(rep(1,s),rep(0,p-s)) # regression coefficient
reg_coef=reg_coef*(2*(rnorm(p)>0)-1)*sig_mag
y=generate_data(X,reg_coef,model) # reponse vector
variable selection for additive model via KKO
Description
The function applys KKO to compute importance scores of components.
Usage
kko(
X,
y,
X_k,
rfn_range = c(2, 3, 4),
n_stb_tune = 50,
n_stb = 100,
cv_folds = 10,
frac_stb = 1/2,
nCores_para = 4,
rkernel = c("laplacian", "gaussian", "cauchy"),
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_tune |
number of subsampling for tuning random feature numbers. |
n_stb |
number of subsampling for computing importance scores. |
cv_folds |
the folds of cross-validation for tuning group lasso penalty. |
frac_stb |
fraction of subsample size. |
nCores_para |
number of cores for parallelizing subsampling. |
rkernel |
kernel choices. Default is "laplacian". Other choices are "cauchy" and "gaussian". |
rk_scale |
scale parameter of sampling distribution for random feature expansion. For gaussian kernel, it is standard deviation of gaussian sampling distribution. |
Value
a list of selection results.
importance_score | importance scores of variables for knockoff filtering. |
selection_frequency | a 0/1 matrix of selection results on subsamples. Rows are subsamples, and columns are variables. The first half columns are variables of design X, and the latter are knockoffs X_k |
rfn_tune | tuned optimal random feature number. |
rfn_range | range of random feature numbers. |
tune_result | a list of tuning results. |
Author(s)
Xiaowu Dai, Xiang Lyu, Lexin Li
Examples
library(knockoff)
p=4 # 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 for importance scores
n_stb_tune=5 # number of subsampling for tuning random feature number
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
kko(X,y,X_k,rfn_range,n_stb_tune,n_stb,cv_folds,frac_stb,nCores_para,rkernel,rk_scale)
nonparametric additive model seleciton via random kernel
Description
The function selects additive components via applying group lasso on random feature expansion of data and knockoffs.
Usage
rk_fit(
X,
y,
X_k,
rfn,
cv_folds,
rkernel = "laplacian",
rk_scale = 1,
rseed = NULL
)
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 |
random feature expansion number. |
cv_folds |
the folds of cross-validation for tuning group lasso penalty. |
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. |
rseed |
seed for random feature expansion. |
Value
a 0/1 vector indicating selected components.
Author(s)
Xiaowu Dai, Xiang Lyu, Lexin Li
Examples
library(knockoff)
p=5 # number of predictors
sig_mag=100 # signal strength
n= 200 # sample size
rkernel="laplacian" # kernel choice
s=2 # sparsity, number of nonzero component functions
rk_scale=1 # scaling paramtere of kernel
rfn= 3 # number of random features
cv_folds=15 # folds of cross-validation in group lasso
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
# the first half is variables of design X, and the latter is knockoffs X_k
rk_fit(X,y,X_k,rfn,cv_folds,rkernel,rk_scale)
compute selection frequency of rk_fit on subsamples
Description
The function applys rk_fit on subsamples and record selection results.
Usage
rk_subsample(
X,
y,
X_k,
rfn,
n_stb,
cv_folds,
frac_stb = 1/2,
nCores_para,
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 |
random feature expansion number. |
n_stb |
number of subsampling. |
cv_folds |
the folds of cross-validation for tuning group lasso. |
frac_stb |
fraction of subsample size. |
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 0/1 matrix indicating selection results. Rows are subsamples, and columns are variables. The first half columns are variables of design X, and the latter are knockoffs X_k.
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= 3 # 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_subsample(X,y,X_k,rfn,n_stb,cv_folds,frac_stb,nCores_para,rkernel,rk_scale)
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)