crossval {quadrupen}

Cross-validation function for quadrupen fitting methods.

Description

Function that computes K-fold (double) cross-validated error of a quadrupen fit. If no lambda2 is provided, simple cross validation on the lambda1 parameter is performed. If a vector lambda2 is passed as an argument, double cross-validation is performed.

Usage

crossval(
  x,
  y,
  penalty = c("elastic.net", "bounded.reg"),
  K = 10,
  folds = split(sample(1:nrow(x)), rep(1:K, length = nrow(x))),
  lambda2 = 0.01,
  verbose = TRUE,
  mc.cores = 2,
  ...
)

Arguments

x

matrix of features, possibly sparsely encoded (experimental). Do NOT include intercept.

y

response vector.

penalty

a string for the fitting procedure used for cross-validation. Either "elastic.net" or "bounded.reg", at the moment. Default is elastic.net.

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, the default scalar value of the corresponding fitting method is used and a simple CV is performed. If a vector of values is given, double cross-validation is performed (both on lambda1 and lambda2, using the same folds for each lambda2).

verbose

logical; indicates if the progression (the current lambda2) should be displayed. Default is TRUE.

mc.cores

the number of cores to use. The default uses 2 cores.

...

additional parameters to overwrite the defaults of the fitting procedure identified by the 'penalty' argument. See the corresponding documentation (elastic.net or bounded.reg).

Value

An object of class "cvpen" for which a plot method is available.

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 many 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.

See Also

quadrupen, plot,cvpen-method and cvpen.

Examples

## 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)

## Use fewer lambda1 values by overwritting the default parameters
## and cross-validate over the sequences lambda1 and lambda2

cv.double <- crossval(x,y, lambda2=10^seq(2,-2,len=50), nlambda1=50)

## Rerun simple cross-validation with the appropriate lambda2
cv.10K <- crossval(x,y, lambda2=0.2)
## Try leave one out also
cv.loo <- crossval(x,y, K=n, lambda2=0.2)


plot(cv.double)

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

## Performance for selection purpose
beta.min.10K <- slot(cv.10K, "beta.min")
beta.min.loo <- slot(cv.loo, "beta.min")

cat("\nFalse positives with the minimal 10-CV choice: ", sum(sign(beta) != sign(beta.min.10K)))
cat("\nFalse positives with the minimal LOO-CV choice: ", sum(sign(beta) != sign(beta.min.loo)))