L2E (version 2.0)

l2e_regression_convex: L2E convex regression - PG

Description

l2e_regression_convex performs L2E convex regression via block coordinate descent with proximal gradient for updating both beta and tau.

Usage

l2e_regression_convex(y, b, tau, max_iter = 100, tol = 1e-04, Show.Time = TRUE)

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)

Arguments

y

Response vector

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

Examples

set.seed(12345)
n <- 200
tau <- 1
x <- seq(-2, 2, length.out=n)
f <- x^4 + x
y <- f + (1/tau) * rnorm(n)

## Clean data example
plot(x, y, pch=16, cex.lab=1.5, cex.axis=1.5, cex.sub=1.5, col='gray')
lines(x, f, lwd=3)

tau <- 1
b <- y
sol <- l2e_regression_convex(y, b, tau)

plot(x, y, pch=16, cex.lab=1.5, cex.axis=1.5, cex.sub=1.5, col='gray')
lines(x, f, lwd=3)
cvx <- fitted(cobs::conreg(y, convex=TRUE))
lines(x, cvx, col='blue', lwd=3)
lines(x, sol$beta, col='dark green', lwd=3)

## Contaminated data example
ix <- 0:9
y[45 + ix] <- 14 + rnorm(10)

plot(x, y, pch=16, cex.lab=1.5, cex.axis=1.5, cex.sub=1.5, col='gray')
lines(x, f, lwd=3)

tau <- 1
b <- y
sol <- l2e_regression_convex(y, b, tau)

plot(x, y, pch=16, cex.lab=1.5, cex.axis=1.5, cex.sub=1.5, col='gray')
lines(x, f, lwd=3)
cvx <- fitted(cobs::conreg(y, convex=TRUE))
lines(x, cvx, col='blue', lwd=3)
lines(x, sol$beta, col='dark green', lwd=3)