Solution path of the L2E trend filtering regression with Lasso

L2E_TF_lasso computes the solution path of the robust trend filtering regression under the L2 criterion with Lasso penalty

L2E_TF_lasso(
  y,
  X,
  beta0,
  tau0,
  D,
  lambdaSeq,
  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
lambdaSeq

A decreasing sequence of values for the tuning parameter lambda, 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 lambda, the run time (vector) for each lambda, and the sequence of lambda used in the regression (vector)

Examples

## Completes in 10 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)
sol <- L2E_TF_lasso(y=y, D=D, lambdaSeq=lambda)

#>    user  system elapsed 
#>   1.002   0.000   1.002 

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[,1], col='blue', lwd=3) ## 1st lambda


## 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_lasso(y=y, D=D, lambdaSeq=lambda)

#>    user  system elapsed 
#>   1.004   0.000   1.005 

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[,1], col='blue', lwd=3) ## 1st lambda