Solution path of the L2E trend filtering regression with distance penalization

L2E_TF_dist computes the solution path of the robust trend filtering regression under the L2 criterion with distance penalty

L2E_TF_dist(
  y,
  X,
  beta0,
  tau0,
  D,
  kSeq,
  rhoSeq,
  max_iter = 100,
  tol = 1e-04,
  Show.Time = 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 D*beta
rhoSeq

An increasing sequence of tuning parameter rho, can be omitted
max_iter

Maximum number of iterations
tol

Relative tolerance
Show.Time

Report the computing time

Value

Returns a list object containing the estimates for beta (matrix) and tau (vector) for each value of the tuning parameter k, the path of estimates for beta (list of matrices) and tau (matrix) for each value of rho, the run time (vector) for each k, and the sequence of rho and k used in the regression (vectors)

Examples

## Completes in 15 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
sol <- L2E_TF_dist(y=y, D=D, kSeq=k, rhoSeq=rho)

#>    user  system elapsed 
#>   0.993   0.000   0.993 
#>    user  system elapsed 
#>   0.682   0.004   0.686 
#>    user  system elapsed 
#>   4.006   0.000   4.008 

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[,3], col='blue', lwd=3) ## k=2

lines(x, sol$Beta[,2], col='red', lwd=3) ## k=3

lines(x, sol$Beta[,1], col='dark green', lwd=3) ## k=4


## 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)


sol <- L2E_TF_dist(y=y, D=D, kSeq=k, rhoSeq=rho)

#>    user  system elapsed 
#>   1.026   0.001   1.026 
#>    user  system elapsed 
#>   0.563   0.000   0.564 
#>    user  system elapsed 
#>   4.022   0.000   4.022 

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[,3], col='blue', lwd=3) ## k=2

lines(x, sol$Beta[,2], col='red', lwd=3) ## k=3

lines(x, sol$Beta[,1], col='dark green', lwd=3) ## k=4