CV_L2E_TF_dist {L2E} | R Documentation |
Cross validation for L2E trend filtering regression with distance penalization
Description
CV_L2E_TF_dist
performs k-fold cross-validation for robust trend filtering regression under the L2 criterion with distance penalty
Usage
CV_L2E_TF_dist(
y,
X,
beta0,
tau0,
D,
kSeq,
rhoSeq,
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 |
kSeq |
A sequence of tuning parameter k, the number of nonzero entries in Dbeta |
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 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 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 20 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)
k <- c(4,3,2)
rho <- 10^8
# (not run)
# cv <- CV_L2E_TF_dist(y=y0, D=D, kSeq=k, rhoSeq=rho, nfolds=2, seed=1234)
# (k_min <- cv$k.min)
# sol <- L2E_TF_dist(y=y0, D=D, kSeq=k_min, rhoSeq=rho)
# plot(x, y, pch=16, cex.lab=1.5, cex.axis=1.5, cex.sub=1.5, col='gray')
# lines(x, f, lwd=3)
# lines(x, sol$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_dist(y=y, D=D, kSeq=k, rhoSeq=rho, nfolds=2, seed=1234)
# (k_min <- cv$k.min)
# sol <- L2E_TF_dist(y=y, D=D, kSeq=k_min, rhoSeq=rho)
# plot(x, y, pch=16, cex.lab=1.5, cex.axis=1.5, cex.sub=1.5, col='gray')
# lines(x, f, lwd=3)
# lines(x, sol$Beta, col='blue', lwd=3)