L2E (version 2.0)

CV_L2E_sparse_ncv: Cross validation for L2E sparse regression with existing penalization methods

Description

CV_L2E_sparse_ncv performs k-fold cross-validation for robust sparse regression under the L2 criterion. Available penalties include lasso, MCP and SCAD.

Usage

CV_L2E_sparse_ncv(
  y,
  X,
  beta0,
  tau0,
  lambdaSeq,
  penalty = "MCP",
  nfolds = 5,
  seed = 1234,
  method = "median",
  max_iter = 100,
  tol = 1e-04,
  trace = TRUE
)

Value

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

Arguments

y

Response vector

X

Design matrix

beta0

Initial vector of regression coefficients, can be omitted

tau0

Initial precision estimate, can be omitted

lambdaSeq

A decreasing sequence of tuning parameter lambda, can be omitted

penalty

Available penalties include lasso, MCP and SCAD.

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

Examples

## Completes in 20 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
lambda <- 10^seq(-1, -2, length.out=20)
# (not run)
# cv <- CV_L2E_sparse_ncv(y=y, X=X, lambdaSeq=lambda, penalty="SCAD", seed=1234, nfolds=2)
# (lambda_min <- cv$lambda.min)

# sol <- L2E_sparse_ncv(y=y, X=X, lambdaSeq=lambda_min, penalty="SCAD")
# 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_ncv(y=y, X=X, lambdaSeq=lambda, penalty="SCAD", seed=1234, nfolds=2)
# (lambda_min <- cv$lambda.min)

# sol <- L2E_sparse_ncv(y=y, X=X, lambdaSeq=lambda_min, penalty="SCAD")
# 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)