L2E_sparse_dist {L2E}

Solution path of L2E sparse regression with distance penalization

Description

L2E_sparse_dist computes the solution path of the robust sparse regression under the L2 criterion with distance penalty

Usage

L2E_sparse_dist(
  y,
  X,
  beta0,
  tau0,
  kSeq,
  rhoSeq,
  stepsize = 0.9,
  sigma = 0.5,
  max_iter = 100,
  tol = 1e-04,
  Show.Time = TRUE
)

Arguments

y

Response vector

X

Design matrix

beta0

Initial vector of regression coefficients, can be omitted

tau0

Initial precision estimate, can be omitted

kSeq

A sequence of tuning parameter k, the number of nonzero entries in the estimated coefficients

rhoSeq

An increasing sequence of tuning parameter rho, can be omitted

stepsize

The stepsize parameter for the MM algorithm (0, 1)

sigma

The halving parameter sigma (0, 1)

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

set.seed(12345)
n <- 100
tau <- 1
f <- matrix(c(rep(2,5), rep(0,45)), ncol = 1)
X <- X0 <- matrix(rnorm(n*50), nrow = n)
y <- y0 <- X0 %*% f + (1/tau)*rnorm(n)

## Clean Data
k <- 5
sol <- L2E_sparse_dist(y=y, X=X, kSeq=k)
r <- y - X %*% sol$Beta
ix <- which(abs(r) > 3/sol$Tau)
l2e_fit <- X %*% sol$Beta

plot(y, l2e_fit, ylab='Predicted values', pch=16, cex=0.8)
points(y[ix], l2e_fit[ix], pch=16, col='blue', cex=0.8)

## Contaminated Data
i <- 1:5
y[i] <- 2 + y0[i]
X[i,] <- 2 + X0[i,]

sol <- L2E_sparse_dist(y=y, X=X, kSeq=k)
r <- y - X %*% sol$Beta
ix <- which(abs(r) > 3/sol$Tau)
l2e_fit <- X %*% sol$Beta

plot(y, l2e_fit, ylab='Predicted values', pch=16, cex=0.8)
points(y[ix], l2e_fit[ix], pch=16, col='blue', cex=0.8)