Cross-validation for Quadrupen object — cross

Function that computes K-fold cross-validated error of a quadrupen fit, possibly on a grid of lambda1, lambda2.

Usage

cross_validate(
  object,
  K = 10,
  folds = split(sample(1:object$nobs), rep(1:K, length = object$nobs)),
  lambda2 = object$minor_tuning,
  verbose = TRUE,
  cores = parallel::detectCores() - 2
)

# S3 method for class 'QuadrupenFit'
cross_validate(
  object,
  K = 10,
  folds = split(sample(1:object$nobs), rep(1:K, length = object$nobs)),
  lambda2 = object$minor_tuning,
  verbose = TRUE,
  cores = parallel::detectCores() - 2
)

Arguments

object: an R6 object with class QuadrupenFit
K: integer indicating the number of folds. Default is 10.
folds: list of K vectors that describes the folds to use for the cross-validation. By default, the folds are randomly sampled with the specified K. The same folds are used for each values of lambda2.
lambda2: tunes the \(\ell_2\)-penalty (ridge-like) of the fit. If none is provided, a vector of values is generated and a CV is performed on a grid of lambda2 and lambda1, using the same folds for each lambda2.
verbose: logical; indicates if the progression (the current lambda2 should be displayed. Default is TRUE.
cores: the number of cores to use. The default uses all the cores available.

Value

an object with class CrossValidation is sent back and stored as a field of the original QuadrupenFit object.

Methods (by class)

cross_validate(QuadrupenFit): S3 method for cross-validation of a QuadrupenFit

Note

If the user runs the fitting method with option 'bulletproof' set to FALSE, the algorithm may stop at an early stage of the path. Early stops are handled internally, in order to provide results on the same grid of penalty tuned by \(\lambda_1\). This is done by means of NA values, so as mean and standard error are consistently evaluated. If, while cross-validating, the procedure experiences too much early stoppings, a warning is sent to the user, in which case you should reconsider the grid of lambda1 used for the cross-validation. If bulletproof is TRUE (the default), there is nothing to worry about, except a possible slow down when any switching to the proximal algorithm is required.

Examples

if (FALSE) { # \dontrun{
## Simulating multivariate Gaussian with blockwise correlation
## and piecewise constant vector of parameters
beta <- rep(c(0,1,0,-1,0), c(25,10,25,10,25))
cor  <- 0.75
Soo  <- toeplitz(cor^(0:(25-1))) ## Toeplitz correlation for irrelevant variable
Sww  <- matrix(cor,10,10) ## bloc correlation between active variables
Sigma <- bdiag(Soo,Sww,Soo,Sww,Soo) + 0.1
diag(Sigma) <- 1
n <- 100
x <- as.matrix(matrix(rnorm(95*n),n,95) %*% chol(Sigma))
y <- 10 + x %*% beta + rnorm(n,0,10)

enet <- elastic.net(x, y, nlambda1=50)

## Use fewer lambda1 values by overwritting the default parameters
## and cross-validate over the sequences lambda1 and lambda2
cv.grid <- cross_validate(enet, lambda2=10^seq(2,-2,len=50))
## Rerun simple cross-validation with the appropriate lambda2
cv.10K <- crossval(x,y, lambda2=cv.grid$lambda2_min)
## Try leave one out also
cv.loo <- crossval(x,y, K=n, lambda2=cv.grid$lambda2_min)

plot(cv.grid)
plot(cv.10K)
plot(cv.loo)

## Performance for selection purpose
cat("\nFalse positives with the minimal 10-CV choice: ", sum(sign(beta) != sign(cv.10K$beta_min )))
cat("\nFalse positives with the minimal LOO-CV choice: ", sum(sign(beta) != sign(cv.loo$beta_min)))
} # }