L2E multivariate regression - PG

l2e_regression performs L2E multivariate regression via block coordinate descent with proximal gradient for updating both beta and tau.

l2e_regression(y, X, b, tau, max_iter = 100, tol = 1e-04, Show.Time = TRUE)

Arguments

y

Response vector
X

Design matrix
b

Initial vector of regression coefficients
tau

Initial precision estimate
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 (vector) and tau (scalar), the number of outer block descent iterations until convergence (scalar), and the number of inner iterations per outer iteration for updating beta and tau (vectors)

Examples

# Bank data example
y <- bank$y
X <- as.matrix(bank[,1:13])
X0 <- as.matrix(cbind(rep(1,length(y)), X))
tauinit <- 1/mad(y)
binit <- matrix(0, 14, 1)

sol <- l2e_regression(y, X0, binit, tauinit)

#>    user  system elapsed 
#>   0.018   0.000   0.018 
r <- y - X0 %*% sol$beta
ix <- which(abs(r) > 3/sol$tau)
l2e_fit <- X0 %*% 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)