CV_L2E_sparse_dist {L2E}

Cross validation for L2E sparse regression with distance penalization

Description

CV_L2E_sparse_dist performs k-fold cross-validation for robust sparse regression under the L2 criterion with distance penalty

Usage

CV_L2E_sparse_dist(
  y,
  X,
  beta0,
  tau0,
  kSeq,
  rhoSeq,
  nfolds = 5,
  seed = 1234,
  method = "median",
  max_iter = 100,
  tol = 1e-04,
  trace = TRUE
)

Arguments

y

Response vector

X

Design matrix

beta0

Initial vector of regression coefficients, can be omitted

tau0

Initial precision estimate, can be omitted

kSeq

A sequence of tuning parameter k, the number of nonzero entries in the estimated coefficients

rhoSeq

A sequence of tuning parameter rho, can be omitted

nfolds

The number of cross-validation folds. Default is 5.

seed

Users can set the seed of the random number generator to obtain reproducible results.

method

Median or mean to compute the objective

max_iter

Maximum number of iterations

tol

Relative tolerance

trace

Whether to trace the progress of the cross-validation

Value

Returns a list object containing the mean and standard error of the cross-validation error (vectors) – CVE and CVSE – for each value of k, the index of the k value with the minimum CVE and the k value itself (scalars), the index of the k value with the 1SE CVE and the k value itself (scalars), the sequence of rho and k used in the regression (vectors), and a vector listing which fold each element of y was assigned to

Examples

## Completes in 15 seconds

set.seed(12345)
n <- 100
tau <- 1
f <- matrix(c(rep(2,5), rep(0,45)), ncol = 1)
X <- X0 <- matrix(rnorm(n*50), nrow = n)
y <- y0 <- X0 %*% f + (1/tau)*rnorm(n)

## Clean Data
k <- c(6,5,4)
# (not run)
# cv <- CV_L2E_sparse_dist(y=y, X=X, kSeq=k, nfolds=2, seed=1234)
# (k_min <- cv$k.min) ## selected number of nonzero entries

# sol <- L2E_sparse_dist(y=y, X=X, kSeq=k_min)
# r <- y - X %*% sol$Beta
# ix <- which(abs(r) > 3/sol$Tau)
# l2e_fit <- X %*% sol$Beta

# plot(y, l2e_fit, ylab='Predicted values', pch=16, cex=0.8)
# points(y[ix], l2e_fit[ix], pch=16, col='blue', cex=0.8)

## Contaminated Data
i <- 1:5
y[i] <- 2 + y0[i]
X[i,] <- 2 + X0[i,]

# (not run)
# cv <- CV_L2E_sparse_dist(y=y, X=X, kSeq=k, nfolds=2, seed=1234)
# (k_min <- cv$k.min) ## selected number of nonzero entries

# sol <- L2E_sparse_dist(y=y, X=X, kSeq=k_min)
# r <- y - X %*% sol$Beta
# ix <- which(abs(r) > 3/sol$Tau)
# l2e_fit <- X %*% sol$Beta

# plot(y, l2e_fit, ylab='Predicted values', pch=16, cex=0.8)
# points(y[ix], l2e_fit[ix], pch=16, col='blue', cex=0.8)