LUM.R

# Large-margin Unified Machine (LUM)
# For single regression

lum <- function(x, y, a = 1, c = 1, lambda = 1, max.iter=100, eps = 1.0e-8){
  # x: predictor
  # y: binary response with {-1, 1} coding
  # a, c: constants in LUM loss
  # lambda: regularization pamameter
  
  V <- function(u, a = 1, c = 1){
    ifelse(u<c/(1+c),(1-u),(1/(1+c))*(a/((1+c)*u-c+a))^a)
  }
  
  coef <- glm(y~x)$coefficient
  alpha <- coef[1]; beta <- coef[2]
  for(iter in 1:max.iter){
    new.beta <- optimize(f= function(bet) 1/n*sum(V(y*(alpha+x*bet), a, c))+lambda/2*bet^2, 
                         interval = c(-100, 100))$minimum
    new.alpha <- optimize(f= function(alp) sum(V(y*(alp + x*new.beta), a, c)), 
                          interval=c(-100, 100))$minimum
    if(max(abs(c(new.alpha, new.beta)-c(alpha, beta))) < eps){
      break}
    beta <- new.beta
    alpha <- new.alpha 
  }
  est <- c(alpha=new.alpha, beta=new.beta) # linear LUM estimator
  return(est)
}