Last updated: 2022-12-06

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Here we illustrate how to use the perform_cv cross-validation interface to estimate the penalty strength paramter in the Elastic Net model in glmnet. Of course, glmnet already has a cross-validation interface, so we can use the existing cross-validation function in glmnet to verify our implementation. Indeed, perform_cv almost exactly reproduces the cv.glmnet output in this example.

Load a couple packages and the perform_cv code.

library(glmnet)
library(parallel)
source("../code/cv.R")

Initialize the sequence of pseudorandom numbers.

set.seed(1)

Simulate a regression data set.

n <- 200
p <- 1000
X <- matrix(rnorm(n*p),n,p)
b <- rep(0,p)
b[sample(p,4)] <- c(1,-1,1,-1)
y <- X %*% b + rnorm(n)

To perform cross-validation, we need to define three functions: (1) a function to fit an Elastic Net model; (2) a function to predict Y using the fitted Elastic Net model; and (3) a function to evaluate the accuracy of the predicted Y (here we use the mean-squared error, which is also what is used in the glmnet package to evaluate the predictions).

This function fits an Elastic Net model:

fit_glmnet <- function (x, y, cvpar, noncvpar, init)
  glmnet(x,y,lambda = cvpar,alpha = 0.5)

This function predicts Y using the fitted Elastic Net model:

predict_glmnet <- function (x, model)
  predict(model,x)

This function computes the mean squared error (MSE) between the predicted and true Y:

compute_mse <- function (pred, true)
  mean((pred - true)^2)

Having defined these three functions, we are ready to use perform_cv:

lambda <- round(rev(exp(seq(-3.75,0.85,length.out = 100))),digits = 4)
t0 <- proc.time()
cv <- perform_cv(fit_glmnet,predict_glmnet,compute_mse,X,y,lambda,nc = 2)
t1 <- proc.time()
print(t1 - t0)
#    user  system elapsed 
#   5.291   0.549   3.475

Compare the result with the result obtained from running cv.glmnet on the same data (the dark blue line is the cv.glmnet result, and the dashed orange line is our result):

par(mar = c(4,4,0,0))
res <- cv.glmnet(X,y,alpha = 0.5)
plot(res$lambda,res$cvm,type = "l",col = "darkblue",lwd = 2,log = "x",
     xlab = "lambda",ylab = "mse")
lines(lambda,rowMeans(cv),col = "darkorange",lwd = 2,lty = "dashed")

Version Author Date
0900606 Peter Carbonetto 2022-12-06 

sessionInfo()
# R version 3.6.2 (2019-12-12)
# Platform: x86_64-apple-darwin15.6.0 (64-bit)
# Running under: macOS Catalina 10.15.7
# 
# Matrix products: default
# BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
# LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
# 
# locale:
# [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
# 
# attached base packages:
# [1] parallel  stats     graphics  grDevices utils     datasets  methods  
# [8] base     
# 
# other attached packages:
# [1] glmnet_4.0-2 Matrix_1.4-2
# 
# loaded via a namespace (and not attached):
#  [1] Rcpp_1.0.8        highr_0.8         pillar_1.6.2      compiler_3.6.2   
#  [5] bslib_0.3.1       later_1.0.0       jquerylib_0.1.4   git2r_0.29.0     
#  [9] workflowr_1.7.0.3 iterators_1.0.12  tools_3.6.2       digest_0.6.23    
# [13] lattice_0.20-38   jsonlite_1.7.2    evaluate_0.14     lifecycle_1.0.0  
# [17] tibble_3.1.3      pkgconfig_2.0.3   rlang_0.4.11      foreach_1.4.7    
# [21] yaml_2.2.0        xfun_0.29         fastmap_1.1.0     stringr_1.4.0    
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# [33] fansi_0.4.0       survival_3.1-8    rmarkdown_2.11    magrittr_2.0.1   
# [37] whisker_0.4       splines_3.6.2     codetools_0.2-16  backports_1.1.5  
# [41] promises_1.1.0    ellipsis_0.3.2    htmltools_0.5.2   shape_1.4.4      
# [45] httpuv_1.5.2      utf8_1.1.4        stringi_1.4.3     crayon_1.4.1