The elementwise Huber function, \(Huber(x, M) = 1\)
for \(|x| \geq |M|\)
for \(|x| \leq |M|.\)
huber(x, M = 1)An Expression, vector, or matrix.
(Optional) A positive scalar value representing the threshold. Defaults to 1.
An Expression representing the Huber function evaluated at the input.
set.seed(11)
n <- 10
m <- 450
p <- 0.1 # Fraction of responses with sign flipped
# Generate problem data
beta_true <- 5*matrix(stats::rnorm(n), nrow = n)
X <- matrix(stats::rnorm(m*n), nrow = m, ncol = n)
y_true <- X %*% beta_true
eps <- matrix(stats::rnorm(m), nrow = m)
# Randomly flip sign of some responses
factor <- 2*rbinom(m, size = 1, prob = 1-p) - 1
y <- factor * y_true + eps
# Huber regression
beta <- Variable(n)
obj <- sum(huber(y - X %*% beta, 1))
prob <- Problem(Minimize(obj))
result <- solve(prob)
result$getValue(beta)
#> [,1]
#> [1,] -2.8809598
#> [2,] 0.1535914
#> [3,] -7.4980147
#> [4,] -6.8611676
#> [5,] 5.8162832
#> [6,] -4.6080355
#> [7,] 6.5681235
#> [8,] 3.1077124
#> [9,] -0.2235099
#> [10,] -4.8797994