l2e_regression_isotonic {L2E}

L2E isotonic regression - PG

Description

l2e_regression_isotonic performs L2E isotonic regression via block coordinate descent with proximal gradient for updating both beta and tau.

Usage

l2e_regression_isotonic(
  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(-2.5, 2.5, length.out=n)
f <- x^3
y <- f + (1/tau)*rnorm(n)

# 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)

tau <- 1
b <- y
sol <- l2e_regression_isotonic(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)
iso <- isotone::gpava(1:n, y)$x
lines(x, iso, col='blue', lwd=3)
lines(x, sol$beta, col='dark green', lwd=3)

# Contaminated Data
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_isotonic(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)
iso <- isotone::gpava(1:n, y)$x
lines(x, iso, col='blue', lwd=3)
lines(x, sol$beta, col='dark green', lwd=3)