Cross validation for L2E trend filtering regression with Lasso penalization

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

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)
cv <- CV_L2E_TF_lasso(y=y0, D=D, lambdaSeq=lambda, nfolds=2, seed=1234)
#> Starting CV fold #1
#> Starting CV fold #2
(lambda_min <- cv$lambda.min)
#> [1] 0.01

sol <- L2E_TF_lasso(y=y0, D=D, lambdaSeq=lambda_min)
#>    user  system elapsed 
#>   0.073   0.004   0.077 

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)

cv <- CV_L2E_TF_lasso(y=y, D=D, lambdaSeq=lambda, nfolds=2, seed=1234)
#> Starting CV fold #1
#> Starting CV fold #2
(lambda_min <- cv$lambda.min)
#> [1] 0.08858668

sol <- L2E_TF_lasso(y=y, D=D, lambdaSeq=lambda_min)
#>    user  system elapsed 
#>   0.063   0.000   0.063 

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)