Vignette for Splitknockoff
Author : Haoxue Wang, Yang Cao, Xinwei Sun, Yuan Yao
Introduction
Split Knockoff is a novel method for controlling the false discovery rate (FDR) in structural sparsity setting. This proposed scheme relaxes the linear subspace constraint to its neighborhood, often known as variable splitting in optimization. This vignette illustrates the usage of Splitknockoff with simulation experiments and will help you apply the split knockoff method in a light way. On top of that, an application to Alzheimer’s Disease study with MRI data demonstrates that the split knockoff method can disclose important lesion regions in brains associated with the disease and connections between neighboring regions of high contrast variations during disease progression.
install.packages("SplitKnockoff") # just one line code to install our packageThere is another Matlab package available. Simulation experiment of both packages verify the conclusion of the paper. This R package is more convenient when applied to new dataset as glmnet can be used directly by
install.packages("glmnet'") # just one line code to install the glmnet toolPlease update your glmnet package to the latest version for smooth usage of this package, this simulation uses glmnet 4.2
For more information, please see the manual inside this package.
Key function
splitknockoff.filter(X, D, y, option) : Split Knockoff filter for structural sparsity problem.
splitknockoff.select(W, q): this function is for variable selection based on W statistics.
function involved frequently
private.hittingpoint(coef, lambda_vec): calculate the hitting time and the sign of respective variable in a path.
simu_unit(n, p, D, A, c, k, option): the simulation unit for simulation experiments.
split_knockoffs.create(X, y, D, nu, option): create a knockoff copy for A_gamma
split_knockoffs.statistics.pathorder.W_path(X, D, y, nu, option): generate the knockoff statistics W for beta from a split LASSO path in the intercepetion assignment step, using the method of path order.
Simulation Results
Figure 1b of the paper, comparing the different distributions of Knockoff statistics and Split Knockoff statistics.
Figure 2a of the paper, FDR in \(D_1\)
Figure 2b of the paper, Power in \(D_1\)
Figure 2b of the paper, FDR in \(D_2\)
Figure 2b of the paper, Power in \(D_2\)
Figure 2b of the paper, FDR in \(D_3\)
Figure 2b of the paper, Power in \(D_3\)
Figure 3a of the paper, Effect of Feature Correlation: FDR for q = 0.2
Figure 3b of the paper, Effect of Feature Correlation: Power for q = 0.2
Figure 4a of the paper, Effect of SNR: FDR for q = 0.2
Figure 4b of the paper, Effect of SNR: Power for q = 0.2
Figure 5a of the paper, Effect of Sparsity Level: FDR for q = 0.2
Figure 5b of the paper, Effect of Sparsity Level: Power and FDR for q = 0.2
For a complete reproduction of the simulation, you can see the code as fellow.
simulation details
Install all the packages and library them.
install.packages("SplitKnockoff") # install our package
library(latex2exp)
library(ggplot2)
library(Matrix)
library(glmnet)
library(MASS)
library(SplitKnockoff)set the parameter for the simulation
k <- 20 # sparsity level
A <- 1 # magnitude
n <- 350 # sample size
p <- 100 # dimension of variables
c <- 0.5 # feature correlation
sigma <-1 # noise level
option <- array(data = NA, dim = length(data), dimnames = NULL)
option$q <- 0.2
option$eta <- 0.1
option$method <- 'knockoff'
option$stage0 <- 'path'
option$normalize <- 'true'
option$cv_rule <- 'min'
option$lambda <- 10.^seq(0, -6, by=-0.01)
option$nu <- 10
option$copy <- 'true'
option <- option[-1]generate D and X
D <- diag(p)
m <- nrow(D)
# generate X
Sigma = matrix(0, p, p)
for( i in 1: p){
for(j in 1: p){
Sigma[i, j] <- c^(abs(i - j))
}
}package mvtnorm needed for this generation, please install it in advance
library(mvtnorm) # package mvtnorm needed for this generation
set.seed(100)
X <- rmvnorm(n,matrix(0, p, 1), Sigma) # generate Xgenerate beta and gamma
beta_true <- matrix(0, p, 1)
for( i in 1: k){
beta_true[i, 1] = A
if ( i%%3 == 1){
beta_true[i, 1] = -A
}
}
gamma_true <- D %*% beta_true
S0 <- which(gamma_true!=0)generate varepsilon and noise and y
# generate varepsilon
set.seed(1)
# generate noise and y
varepsilon <- rnorm(n) * sqrt(sigma)
y <- X %*% beta_true + varepsilonkey step
use the key function filter to get the Z_path and t_Z_path
## Split Knockoff
filter_result <- splitknockoff.filter(X, D, y, option)
Z_path <- filter_result$Z
t_Z_path <- filter_result$t_Zplot the figure
a <- sub("TRUE","0",is.element(1:m, S0))
b <- sub("FALSE","1",a)
df <- data.frame(x=Z_path[[1]],y= t_Z_path[[1]], feature=b)
save.image("C:/Users/v-haoxuewang/Desktop/SplitKnockoff/simu_experiments/figure_1/result/figure_1.RData")
png(file='C:/Users/v-haoxuewang/Desktop/SplitKnockoff/simu_experiments/figure_1/plot/figure_1b.png', height=1000, width=1000)
p <- ggplot(data=df,aes(x=x, y=y, color=feature))+geom_point(size=2)
p <-p + labs(title = "Split Knockoff with Lasso Statistic")
p <-p + labs(x = TeX("Value of $Z_i$"))
p <-p + labs(y = TeX("Value of $\\tilde{Z_i}$"))
p <-p + scale_fill_discrete(breaks=c("Null feature","Non-null feature"))
p <-p + geom_abline(intercept=0,slope=1 )
p <-p + scale_colour_discrete(labels=c("Null feature", "Non-null feature"))
p <-p + scale_y_continuous(limits = c(0, Z_path[[1]]))
print(p)
dev.off()here we see the result
for Figure 2a, 2b, 2d, 2e, 2g and 2h of the paper simulation
# 1 June, 2021
# revised 7 July, 2021
# author：Haoxue Wang (haoxwang@student.ethz.ch)
# This script reproduces the figures of FDR and power in Section 5.2, 5.3, 5.4
# of the paper, comparing the performance of Split Knockoffs and Knockoffs.
#
# The intermediate result will be automatically saved to
# '../result/temp.RData’ with the proceeding of the calculation. The final
# result will be saved to '../result/examples.mat'. The whole calculation
# may takes hours to finish.
install.packages("SplitKnockoff") # install our package
library(latex2exp)
library(ggplot2)
library(Matrix)
library(glmnet)
library(MASS)
library(SplitKnockoff)
k <- 20 # sparsity level
A <- 1 # magnitude
n <- 350 # sample size
p <- 100 # dimension of variables
c <- 0.5 # feature correlation
option <- array(data=NA, dim = length(data), dimnames = NULL)
option$q <- 0.2
option$eta <- 0.1
option$stage0 <- 'path'
option$normalize <- 'true'
option$lambda <- 10.^seq(0, -6, by=-0.01)
option$copy <- 'true'
option <- option[-1]
# settings for nu
expo <- seq(-1, 3, by=0.2)
option$nu <- 10.^expo
num_nu <- length(option$nu)
## calculation
# generate D1, D2, and D3
D_G = matrix(0,p-1, p)
for (i in 1:p-1){
D_G[i, i] <- 1
D_G[i, i+1] <- -1
}
D_1 <-diag(p)
D_2 <- D_G
D_3 <- rbind(diag(p), D_G)
D_s <- array(data = NA, dim = length(data), dimnames = NULL)
D_s$D_1 <- D_1
D_s$D_2 <- D_2
D_s$D_3 <- D_3
D_s <- D_s[-1]
fdr_split <- array(0,c(3, num_nu, 2))
power_split <- array(0,c(3, num_nu,2))
# fdr_knock <- matrix(0, 2, 2)
# power_knock <- matrix(0, 2, 2)
num_method <- 2
method_s <- c('knockoff', 'knockoff+')
# attention! for quick speed, please set the meth manually 1 and 2
# when meth =2, set the ratio calculation offset=1 in function select
meth = 1
for (i in 1: 3){
# choose the respective D for each example
sprintf('Running example for D_%d', i)
D <- D_s[[i]]
simu_data <- simu_unit(n, p, D, A, c, k, option)
fdr_split[i, , meth ] <- simu_data$fdr_split
power_split[i, , meth] <- simu_data$power_split
# if (i < 3){
# fdr_knock[meth, i] <- simu_data$fdr_knock
# power_knock[meth, i] <- simu_data$power_knock
# }
}
save.image(file = "C:/Users/v-haoxuewang/Desktop/SplitKnockoff/simu_experiments/examples/result/temp.RData")
# save results
save.image("C:/Users/v-haoxuewang/Desktop/SplitKnockoff/simu_experiments/examples/result/examples.RData")
fdr_split_result <- fdr_split
power_split_result <- power_split
## for D_1
## plot for FDR
x <- expo
fdr_split <- fdr_split_result[1, ,1]
fdr_split <- array(fdr_split, dim=c(num_nu, 1))
fdr_split_plus <- fdr_split_result[1,,2]
fdr_split_plus <- array(fdr_split_plus, dim=c(num_nu, 1))
fdr <- data.frame(x,fdr_split,fdr_split_plus)
fdr[is.na(fdr)] <- 0
png(file='C:/Users/v-haoxuewang/Desktop/SplitKnockoff/simu_experiments/examples/plot/figure_11.png', height=1000, width=1000)
p <- ggplot()+geom_line(data=fdr,aes(x=x, y=fdr_split, color='fdr_split'))
p <- p +geom_line(data=fdr,aes(x=x, y=fdr_split_plus, color='fdr_split_plus'))
p <-p + labs(x = TeX("$\\log_{10} (\\nu)$"))
p <-p + labs(y = TeX("FDR"))
p <-p + geom_abline(intercept=0.2,slope=0,linetype="dashed" )
p <-p + scale_fill_discrete(breaks=c("split Knockoff", "split Knockoff+"))
p <-p + scale_colour_discrete(labels=c("split Knockoff", "split Knockoff+"))
p <-p + scale_y_continuous(limits = c(0,1))
print(p)
dev.off()
## plot for Power
x <- expo
power_split <- power_split_result[1,,1]
power_split <- array(power_split, dim=c(num_nu, 1))
power_split_plus <- power_split_result[1,,2]
power_split_plus <- array(power_split_plus, dim=c(num_nu, 1))
power <- data.frame(x, power_split,power_split_plus)
png(file='C:/Users/v-haoxuewang/Desktop/SplitKnockoff/simu_experiments/examples/plot/figure_12.png', height=1000, width=1000)
q <- ggplot()+geom_line(data=power,aes(x=x, y=power_split, color='split Knockoff'))
q <- q + geom_line(data=power,aes(x=x, y=power_split_plus, color='split Knockoff+'))
q <-q + labs(x = TeX("$\\log_{10} (\\nu)$"))
q <-q + labs(y = TeX("Power"))
q <-q + scale_fill_discrete(breaks=c("split Knockoff", "split Knockoff+"))
q <-q + scale_colour_discrete(labels=c("split Knockoff", "split Knockoff+"))
q <-q+ scale_y_continuous(limits = c(0,1))
print(q)
dev.off()
## for D_2
## plot for FDR
x <- expo
fdr_split <- fdr_split_result[2,,1]
fdr_split <- array(fdr_split, dim=c(num_nu, 1))
fdr_split_plus <- fdr_split_result[2, ,2]
fdr_split_plus <- array(fdr_split_plus, dim=c(num_nu, 1))
fdr <- data.frame(x,fdr_split,fdr_split_plus)
fdr[is.na(fdr)] <- 0
# save results
png(file='C:/Users/v-haoxuewang/Desktop/SplitKnockoff/simu_experiments/examples/plot/figure_21.png', height=1000, width=1000)
p <- ggplot()+geom_line(data=fdr,aes(x=x, y=fdr_split, color='fdr_split'))
p <- p +geom_line(data=fdr,aes(x=x, y=fdr_split_plus, color='fdr_split_plus'))
p <-p + labs(x = TeX("$\\log_{10} (\\nu)$"))
p <-p + labs(y = TeX("FDR"))
p <-p + geom_abline(intercept=0.2,slope=0,linetype="dashed" )
p <-p + scale_fill_discrete(breaks=c("split Knockoff", "split Knockoff+"))
p <-p + scale_colour_discrete(labels=c("split Knockoff", "split Knockoff+"))
p <-p + scale_y_continuous(limits = c(0,1))
print(p)
dev.off()
## plot for Power
x <- expo
power_split <- power_split_result[2,,1 ]
power_split <- array(power_split, dim=c(num_nu, 1))
power_split_plus <- power_split_result[2,,2]
power_split_plus <- array(power_split_plus, dim=c(num_nu, 1))
# power_knock_ <- power_knock[1]
# power_knock_plus_ <- power_knock[2]
# power_knock_ <- rep(power_knock_, num_nu)
# power_knock_plus_ <- rep(power_knock_plus_, num_nu)
power <- data.frame(x,power_split,power_split_plus)
png(file='C:/Users/v-haoxuewang/Desktop/SplitKnockoff/simu_experiments/examples/plot/figure_22.png', height=1000, width=1000)
q <- ggplot()+geom_line(data=power,aes(x=x, y=power_split, color='power_split'))
q <- q + geom_line(data=power,aes(x=x, y=power_split_plus, color='power_split_plus'))
q <-q + labs(x = TeX("$\\log_{10} (\\nu)$"))
q <-q + labs(y = TeX("Power"))
q <-q + scale_fill_discrete(breaks=c("split Knockoff", "split Knockoff+"))
q <-q+ scale_colour_discrete(labels=c("split Knockoff", "split Knockoff+"))
q <-q+ scale_y_continuous(limits = c(0,1))
print(q)
dev.off()
## for D_3
## plot for FDR
x <- expo
fdr_split <- fdr_split_result[3,,1 ]
fdr_split <- array(fdr_split, dim=c(num_nu, 1))
fdr_split_plus <- fdr_split_result[3,,2]
fdr_split_plus <- array(fdr_split_plus, dim=c(num_nu, 1))
fdr <- data.frame(x,fdr_split,fdr_split_plus)
fdr[is.na(fdr)] <- 0
# save results
png(file='C:/Users/v-haoxuewang/Desktop/SplitKnockoff/simu_experiments/examples/plot/figure_31.png', height=1000, width=1000)
p <- ggplot()+geom_line(data=fdr,aes(x=x, y=fdr_split, color='fdr_split'))
p <- p +geom_line(data=fdr,aes(x=x, y=fdr_split_plus, color='fdr_split_plus'))
p <-p + labs(x = TeX("$\\log_{10} (\\nu)$"))
p <-p + labs(y = TeX("FDR"))
p <-p + geom_abline(intercept=0.2,slope=0,linetype="dashed" )
p <-p + scale_fill_discrete(breaks=c("split Knockoff", "split Knockoff+"))
p <-p + scale_colour_discrete(labels=c("split Knockoff", "split Knockoff+"))
p <-p + scale_y_continuous(limits = c(0,1))
print(p)
dev.off()
## plot for Power
x <- expo
power_split <- power_split_result[3,,1 ]
power_split <- array(power_split, dim=c(num_nu, 1))
power_split_plus <- power_split_result[3,,2]
power_split_plus <- array(power_split_plus, dim=c(num_nu, 1))
power <- data.frame(x,power_split,power_split_plus)
png(file='C:/Users/v-haoxuewang/Desktop/SplitKnockoff/simu_experiments/examples/plot/figure_32.png', height=1000, width=1000)
q <- ggplot()+geom_line(data=power,aes(x=x, y=power_split, color='power_split'))
q <- q + geom_line(data=power,aes(x=x, y=power_split_plus, color='power_split_plus'))
q <-q + labs(x = TeX("$\\log_{10} (\\nu)$"))
q <-q + labs(y = TeX("Power"))
q <-q + scale_fill_discrete(breaks=c("split Knockoff", "split Knockoff+"))
q <-q+ scale_colour_discrete(labels=c("split Knockoff ", "split Knockoff+"))
q <-q+ scale_y_continuous(limits = c(0,1))
print(q)
dev.off()
save.image(file = "C:/Users/v-haoxuewang/Desktop/SplitKnockoff/simu_experiments/examples/result/final.RData")for Figure 3a and 3b of the paper simulation
# simulation experinment
# 1 June, 2021
# revised 7 July, 2021
# author：Haoxue Wang (haoxwang@student.ethz.ch)
# This script reproduces Figure 3 of the paper, comparing the performance
# of Knockoff and Split Knockoff in extreme settings of feature
# correlation.
# The final workspace is saved to '../result/correlation.RData'.
install.packages("SplitKnockoff") # install our package
library(latex2exp)
library(ggplot2)
library(Matrix)
library(glmnet)
library(MASS)
library(SplitKnockoff)
## choose parameters
k <- 20 # sparsity level
A <- 1 # magnitude
n <- 350 # sample size
p <- 100 # dimention of variables
c_s <- c(0, 0.9) # feature correlation
option <- array(data = NA, dim = length(data), dimnames = NULL)
option$q <- 0.2
option$eta <- 0.1
option$method <- 'knockoff'
option$stage0 <- 'path'
option$normalize = 'true'
option$lambda <- 10.^seq(0, -6, by=-0.01)
option$copy = 'true'
## settings for nu
expo = seq(-1, 3, by=0.2)
option$nu = 10.^expo
num_nu = length(option$nu)
## calculation
# generate D
D_G <- matrix(0,p-1, p)
for(i in 1:p-1){
D_G[i, i] <- 1
D_G[i, i+1] <- -1
}
D <- D_G
fdr_glmnet <- matrix(0, 2, num_nu)
power_glmnet <- matrix(0, 2, num_nu)
# fdr_knock <- matrix(0, 2, 1)
# power_knock <- matrix(0, 2, 1)
for(i in 1: 2){
c <- c_s[i]
simu_data <- simu_unit(n, p, D, A, c, k,option)
fdr_glmnet[i, ] <- simu_data$fdr_split
power_glmnet[i, ] <- simu_data$power_split
# fdr_knock[i,] <- simu_data$fdr_knock
# power_knock[i,] <- simu_data$power_knock
}
## plot for FDR
x <- expo
fdr_split <- fdr_glmnet[1, ]
fdr_split <- array(fdr_split, dim=c(num_nu, 1))
fdr_split_plus <- fdr_glmnet[2, ]
fdr_split_plus <- array(fdr_split_plus, dim=c(num_nu, 1))
# fdr_knock_ <- fdr_knock[1]
# fdr_knock_plus_ <- fdr_knock[2]
# fdr_knock_ <- rep(fdr_knock_, num_nu)
# fdr_knock_plus_ <- rep(fdr_knock_plus_, num_nu)
fdr <- data.frame(x,fdr_split,fdr_split_plus)
fdr[is.na(fdr)] <- 0
# save results
save.image("C:/Users/v-haoxuewang/Desktop/SplitKnockoff/simu_experiments/param_ablation/result/correlation.RData")
png(file='C:/Users/v-haoxuewang/Desktop/SplitKnockoff/simu_experiments/param_ablation/plot/figure_3a.png', height=1000, width=1000)
p <- ggplot()+geom_line(data=fdr,aes(x=x, y=fdr_split, color='fdr_split'))
p <- p +geom_line(data=fdr,aes(x=x, y=fdr_split_plus, color='fdr_split_plus'))
p <-p + labs(x = TeX("$\\log_{10} (\\nu)$"))
p <-p + labs(y = TeX("FDR"))
p <-p + geom_abline(intercept=0.2,slope=0,linetype="dashed" )
p <-p + scale_fill_discrete(breaks=c("split Knockoff (c = 0)", "split Knockoff (c = 0.9)"))
p <-p + scale_colour_discrete(labels=c("split Knockoff (c = 0)", "split Knockoff (c = 0.9)"))
p <-p + scale_y_continuous(limits = c(0,1))
print(p)
dev.off()
## plot for Power
x <- expo
power_split <- power_glmnet[1, ]
power_split <- array(power_split, dim=c(num_nu, 1))
power_split_plus <- power_glmnet[2, ]
power_split_plus <- array(power_split_plus, dim=c(num_nu, 1))
# power_knock_ <- power_knock[1]
# power_knock_plus_ <- power_knock[2]
# power_knock_ <- rep(power_knock_, num_nu)
# power_knock_plus_ <- rep(power_knock_plus_, num_nu)
power <- data.frame(x,power_split,power_split_plus)
png(file='C:/Users/v-haoxuewang/Desktop/SplitKnockoff/simu_experiments/param_ablation/plot/figure_3b.png', height=1000, width=1000)
q <- ggplot()+geom_line(data=power,aes(x=x, y=power_split, color='power_split'))
q <- q + geom_line(data=power,aes(x=x, y=power_split_plus, color='power_split_plus'))
q <-q + labs(x = TeX("$\\log_{10} (\\nu)$"))
q <-q + labs(y = TeX("Power"))
q <-q + scale_fill_discrete(breaks=c("split Knockoff (c = 0)", "split Knockoff (c = 0.9)"))
q <-q+ scale_colour_discrete(labels=c("split Knockoff (c = 0)", "split Knockoff (c = 0.9)"))
q <-q+ scale_y_continuous(limits = c(0,1))
print(q)
dev.off()for Figure 4a and 4b of the paper simulation
install.packages("SplitKnockoff") # install our package
library(latex2exp)
library(ggplot2)
library(Matrix)
library(glmnet)
library(MASS)
library(SplitKnockoff)
## choose parameters
k <- 20 # sparsity level
A_s <- c(0.25, 4) #magnitude
n <- 350 # sample size
p <- 100 # dimention of variables
c <- 0.5 # feature correlation
option <- array(data = NA, dim = length(data), dimnames = NULL)
option$q <- 0.2
option$eta <- 0.1
option$method <- 'knockoff'
option$stage0 <- 'path'
option$normalize <- 'true'
option$lambda <- 10.^seq(0, -6, by=-0.01)
option$copy = 'true'
# settings for nu
expo <- seq(-1, 3, by=0.2)
option$nu <- 10.^expo
num_nu <- length(option$nu)
# generate D
D_G <- matrix(0,p-1, p)
for(i in 1:p-1){
D_G[i, i] <- 1
D_G[i, i+1] <- -1
}
D <- D_G
fdr_glmnet <- matrix(0, 2, num_nu)
power_glmnet <- matrix(0, 2, num_nu)
# fdr_knock <- matrix(0, 2, 1)
# power_knock <- matrix(0, 2, 1)
for(i in 1: 2){
A <- A_s[i]
simu_data <- simu_unit(n, p, D, A, c, k, option)
fdr_glmnet[i, ] <- simu_data$fdr_split
power_glmnet[i, ] <- simu_data$power_split
# fdr_knock[i] <- simu_data$fdr_knock
# power_knock[i] <- simu_data$power_knock
}
## plot for FDR
x <- expo
fdr_split <- fdr_glmnet[1, ]
fdr_split <- array(fdr_split, dim=c(num_nu, 1))
fdr_split_plus <- fdr_glmnet[2, ]
fdr_split_plus <- array(fdr_split_plus, dim=c(num_nu, 1))
# fdr_knock_ <- fdr_knock[1]
# fdr_knock_plus_ <- fdr_knock[2]
# fdr_knock_ <- rep(fdr_knock_, num_nu)
# fdr_knock_plus_ <- rep(fdr_knock_plus_, num_nu)
fdr <- data.frame(x,fdr_split,fdr_split_plus)
fdr[is.na(fdr)] <- 0
# save results
save.image("C:/Users/v-haoxuewang/Desktop/SplitKnockoff/simu_experiments/param_ablation/result/snr.RData")
png(file='C:/Users/v-haoxuewang/Desktop/SplitKnockoff/simu_experiments/param_ablation/plot/figure_4a.png', height=1000, width=1000)
p <- ggplot()+geom_line(data=fdr,aes(x=x, y=fdr_split, color='fdr_split'))
p <- p +geom_line(data=fdr,aes(x=x, y=fdr_split_plus, color='fdr_split_plus'))
p <-p + labs(x = TeX("$\\log_{10} (\\nu)$"))
p <-p + labs(y = TeX("FDR"))
p <-p + geom_abline(intercept=0.2,slope=0,linetype="dashed" )
p <-p + scale_fill_discrete(breaks=c("split Knockoff (SNR = 0.25)", "split Knockoff (SNR = 4)"))
p <-p + scale_colour_discrete(labels=c("split Knockoff (SNR = 0.25)", "split Knockoff (SNR = 4)"))
p <-p + geom_abline(intercept=0.2,slope=0,linetype="dashed" )
p <-p + scale_y_continuous(limits = c(0,1))
print(p)
dev.off()
## plot for Power
x <- expo
power_split <- power_glmnet[1, ]
power_split <- array(power_split, dim=c(num_nu, 1))
power_split_plus <- power_glmnet[2, ]
power_split_plus <- array(power_split_plus, dim=c(num_nu, 1))
# power_knock_ <- power_knock[1]
# power_knock_plus_ <- power_knock[2]
# power_knock_ <- rep(power_knock_, num_nu)
# power_knock_plus_ <- rep(power_knock_plus_, num_nu)
power <- data.frame(power_split,power_split_plus)
png(file='C:/Users/v-haoxuewang/Desktop/SplitKnockoff/simu_experiments/param_ablation/plot/figure_4b.png', height=1000, width=1000)
q <- ggplot()+geom_line(data=power,aes(x=x, y=power_split, color='power_split'))
q <- q + geom_line(data=power,aes(x=x, y=power_split_plus, color='power_split_plus'))
q <-q + labs(x = TeX("$\\log_{10} (\\nu)$"))
q <-q + labs(y = TeX("Power"))
q <-q + scale_fill_discrete(breaks=c("split Knockoff (SNR = 0.25)", "split Knockoff (SNR = 4)"))
q <-q+ scale_colour_discrete(labels=c("split Knockoff (SNR = 0.25)", "split Knockoff (SNR = 4)"))
q <-q+ scale_y_continuous(limits = c(0,1))
print(q)
dev.off()
for Figure 5a and 5b of the paper simulation
install.packages("SplitKnockoff") # install our package
library(latex2exp)
library(ggplot2)
library(Matrix)
library(glmnet)
library(MASS)
library(SplitKnockoff)
## choose parameters
k_s <- c(10, 100) # sparsity level
A <- 1 # magnitude
n <- 350 # sample size
p <- 100 # dimention of variables
c <- 0.5 # feature correlation
option <- array(data = NA, dim = length(data), dimnames = NULL)
option$q <- 0.2
option$eta <- 0.1
option$method <- 'knockoff'
option$stage0 <- 'path'
option$normalize <- 'true'
option$lambda <- 10.^seq(0, -6, by=-0.01)
option$copy = 'true'
# settings for nu
expo <- seq(-1, 3, by=0.2)
option$nu <- 10.^expo
num_nu <- length(option$nu)
## calculation
# generate D
D_G <- matrix(0,p-1, p)
for(i in 1:p-1){
D_G[i, i] <- 1
D_G[i, i+1] <- -1
}
D <- D_G
fdr_glmnet <- matrix(0, 2, num_nu)
power_glmnet <- matrix(0, 2, num_nu)
# fdr_knock <- matrix(0, 2, 1)
# power_knock <- matrix(0, 2, 1)
for(i in 1: 2){
k <- k_s[i]
simu_data <- simu_unit(n, p, D, A, c, k, option)
fdr_glmnet[i, ] <- simu_data$fdr_split
power_glmnet[i, ] <- simu_data$power_split
# fdr_knock[i] <- simu_data$fdr_knock
# power_knock[i] <- simu_data$power_knock
}
## plot for FDR
x <- expo
fdr_split <- fdr_glmnet[1, ]
fdr_split <- array(fdr_split, dim=c(num_nu, 1))
fdr_split_plus <- fdr_glmnet[2, ]
fdr_split_plus <- array(fdr_split_plus, dim=c(num_nu, 1))
# fdr_knock_ <- fdr_knock[1]
# fdr_knock_plus_ <- fdr_knock[2]
# fdr_knock_ <- rep(fdr_knock_, num_nu)
# fdr_knock_plus_ <- rep(fdr_knock_plus_, num_nu)
fdr <- data.frame(x,fdr_split,fdr_split_plus)
fdr[is.na(fdr)] <- 0
# save results
save.image("C:/Users/v-haoxuewang/Desktop/SplitKnockoff/simu_experiments/param_ablation/result/sparsity.RData")
png(file='C:/Users/v-haoxuewang/Desktop/SplitKnockoff/simu_experiments/param_ablation/plot/figure_5a.png', height=1000, width=1000)
p <- ggplot()+geom_line(data=fdr,aes(x=x, y=fdr_split, color='fdr_split'))
p <- p +geom_line(data=fdr,aes(x=x, y=fdr_split_plus, color='fdr_split_plus'))
p <-p + labs(x = TeX("$\\log_{10} (\\nu)$"))
p <-p + labs(y = TeX("FDR"))
p <-p + geom_abline(intercept=0.2,slope=0,linetype="dashed" )
p <-p + scale_fill_discrete(breaks=c("split Knockoff (k = 10)", "split Knockoff (k = 100)"))
p <-p + scale_colour_discrete(labels=c("split Knockoff (k = 10)", "split Knockoff (k = 100)"))
p <-p + scale_y_continuous(limits = c(0,1))
print(p)
dev.off()
## plot for Power
x <- expo
power_split <- power_glmnet[1, ]
power_split <- array(power_split, dim=c(num_nu, 1))
power_split_plus <- power_glmnet[2, ]
power_split_plus <- array(power_split_plus, dim=c(num_nu, 1))
# power_knock_ <- power_knock[1]
# power_knock_plus_ <- power_knock[2]
# power_knock_ <- rep(power_knock_, num_nu)
# power_knock_plus_ <- rep(power_knock_plus_, num_nu)
power <- data.frame(power_split,power_split_plus)
png(file='C:/Users/v-haoxuewang/Desktop/SplitKnockoff/simu_experiments/param_ablation/plot/figure_5b.png', height=1000, width=1000)
q <- ggplot()+geom_line(data=power,aes(x=x, y=power_split, color='power_split'))
q <- q + geom_line(data=power,aes(x=x, y=power_split_plus, color='power_split_plus'))
q <-q + labs(x = TeX("$\\log_{10} (\\nu)$"))
q <-q + labs(y = TeX("Power"))
q <-q + scale_fill_discrete(breaks=c("split Knockoff (k = 10)", "split Knockoff (k = 100)"))
q <-q+ scale_colour_discrete(labels=c("split Knockoff (k = 10)", "split Knockoff (k = 100)"))
q <-q+ scale_y_continuous(limits = c(0,1))
q <-q+ scale_y_continuous(limits = c(0,1))
print(q)
dev.off()
Alzheimer’s Disease application
Disclose important lesion regions in brains associated with the disease
library(latex2exp)
library(ggplot2)
library(Matrix)
library(glmnet)
library(MASS)
library(SplitKnockoff)
option <- array(data=NA, dim = length(data), dimnames = NULL)
option$q <- 0.2
option$eta <- 0.1
option$stage0 <- 'path'
option$normalize <- 'true'
option$lambda <- 10.^seq(0, -6, by=-0.01)
option$copy <- 'true'
option <- option[-1]
# settings for nu
expo <- seq(-1, 1, by=0.1)
option$nu <- 10.^expo
num_nu <- length(option$nu)
root = getwd()
setwd(sprintf('%s/data/', root))
X = read.csv('X.csv')
X =as.matrix(X)
y = read.csv('y.csv')
y = as.matrix(y)
D = read.csv('D.csv')
D = as.matrix(D)
D = diag(90)
filter_result <- splitknockoff.filter(X, D, y, option)
results <- filter_result$results
save(results, file="results/region.RData")results of the regions
each number specifies a region
Connections between neighboring regions of high contrast variations during disease progression.
library(latex2exp)
library(ggplot2)
library(Matrix)
library(glmnet)
library(MASS)
library(SplitKnockoff)
option <- array(data=NA, dim = length(data), dimnames = NULL)
option$q <- 0.2
option$eta <- 0.1
option$stage0 <- 'path'
option$normalize <- 'true'
option$lambda <- 10.^seq(0, -6, by=-0.01)
option$copy <- 'true'
option <- option[-1]
# settings for nu
expo <- seq(-1, 1, by=0.1)
option$nu <- 10.^expo
num_nu <- length(option$nu)
# original .mat data
root = getwd()
setwd(sprintf('%s/data/', root))
X = readMat('X.mat')
X = X$X
y = readMat('y.mat')
y = y$y
D = readMat('D.mat')
D = D$D
#
# root = getwd()
# setwd(sprintf('%s/data/', root))
# X = read.csv('X.csv')
# X =as.matrix(X)
# y = read.csv('y.csv')
# y = as.matrix(y)
# D = read.csv('D.csv')
# D = as.matrix(D)
filter_result <- splitknockoff.filter(X, D, y, option)
results <- filter_result$results
save(results, file="results/connection.RData")results of connection
each number specifies a connection
For your consideration
It usually takes 50min-80min to simulate each experiment. If you want to see the result of the experiment directly, you can reload our generated result by
load("...../SplitKnockoff/simu_experiments/figure_1/result/figure_1.RData")
load("...../SplitKnockoff/simu_experiments/param_ablation/result/correlation.RData")
load("...../SplitKnockoff/simu_experiments/param_ablation/result/snr.RData")
load("...../SplitKnockoff/simu_experiments/param_ablation/result/sparsity.RData")
load("...../SplitKnockoff/simu_experiments/examples/result/final.RData")If you have any question or idea, please contact the author of this R package Haoxue Wang (haoxwang@student.ethz.ch).