l2e_regression_convex: L2E convex regression - PG

In jocelynchi/L2E-package-demo: Robust Structured Regression via the L2 Criterion

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)

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

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

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)

jocelynchi/L2E-package-demo documentation built on Oct. 6, 2022, 6:05 a.m.