CV_L2E_TF_lasso {L2E}

Cross validation for L2E trend filtering regression with Lasso penalization

Description

CV_L2E_TF_lasso performs k-fold cross-validation for robust trend filtering regression under the L2 criterion with the Lasso penalty

Usage

CV_L2E_TF_lasso(
  y,
  X,
  beta0,
  tau0,
  D,
  lambdaSeq,
  nfolds = 5,
  seed = 1234,
  method = "median",
  max_iter = 100,
  tol = 1e-04,
  trace = TRUE
)

Arguments

y

Response vector

X

Design matrix. Default is the identity matrix.

beta0

Initial vector of regression coefficients, can be omitted

tau0

Initial precision estimate, can be omitted

D

The fusion matrix

lambdaSeq

A decreasing sequence of tuning parameter lambda, 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 calculate the objective value

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 – 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

Examples

## Completes in 30 seconds

set.seed(12345)
n <- 100
x <- 1:n
f <- matrix(rep(c(-2,5,0,-10), each=n/4), ncol=1)
y <- y0 <- f + rnorm(length(f))

## Clean Data
plot(x, y, pch=16, cex.lab=1.5, cex.axis=1.5, cex.sub=1.5, col='gray')
lines(x, f, lwd=3)

D <- myGetDkn(1, n)
lambda <- 10^seq(-1, -2, length.out=20)
# (not run)
# cv <- CV_L2E_TF_lasso(y=y0, D=D, lambdaSeq=lambda, nfolds=2, seed=1234)
# (lambda_min <- cv$lambda.min)

# sol <- L2E_TF_lasso(y=y0, D=D, lambdaSeq=lambda_min)

# plot(x, y, pch=16, cex.lab=1.5, cex.axis=1.5, cex.sub=1.5, col='gray')
# lines(x, f, lwd=3)
# lines(x, sol$Beta, col='blue', lwd=3)

## Contaminated Data
ix <- sample(1:n, 10)
y[ix] <- y0[ix] + 2

plot(x, y, pch=16, cex.lab=1.5, cex.axis=1.5, cex.sub=1.5, col='gray')
lines(x, f, lwd=3)

# (not run)
# cv <- CV_L2E_TF_lasso(y=y, D=D, lambdaSeq=lambda, nfolds=2, seed=1234)
# (lambda_min <- cv$lambda.min)

# sol <- L2E_TF_lasso(y=y, D=D, lambdaSeq=lambda_min)

# plot(x, y, pch=16, cex.lab=1.5, cex.axis=1.5, cex.sub=1.5, col='gray')
# lines(x, f, lwd=3)
# lines(x, sol$Beta, col='blue', lwd=3)