L2E isotonic regression - PG

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

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)

#>    user  system elapsed 
#>   0.242   0.000   0.243 

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)

#>    user  system elapsed 
#>   0.132   0.000   0.132 

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)