Analytical solution to Logistic Kernel Ridge Regression problem, optimized to reduce alpha to within argument 'tol'. Arguments: K = Gram or kernel matrix, y = response, lambda = regularizing coefficient, maxiter = maximum number of iterations, tol = tolerance for reducing alpha parameters

Optimized_Logistic_Kernel_Ridge_Regression.R

KRR_logit_optim <- function(K, y, lambda, maxiter = 100, tol = 0.01){
  # LOGISTIC - optimize alpha
  # example: KRR_logit_optim(K, y, 0.1, 100, 0.01)
   N = nrow(K)
  alpha = rep(1/N, N) # initialize alpha value
  iter = 1
  while (TRUE) {
    Kalpha = as.vector(K %*% alpha)
    spec = 1 + exp(-Kalpha)
    pi = 1 / spec
    diagW = pi * (1 - pi)
    e = (presence - pi) / diagW
    q = Kalpha + e
    theSol = try(solve(K + lambda * Diagonal(x=1/diagW), q))
    if (class(theSol) == "try-error") {
      break
    }
    alphan = as.vector(theSol)
    if (any(is.nan(alphan)) || all(abs(alphan - alpha) <= tol)) {
      break
    }
    else if (iter > maxiter) {
      cat("klogreg:maxiter!")
      break
    }
    else {
      alpha = alphan
      iter = iter + 1
    }
  }
  log_pred <-  1 / (1 + exp(-as.vector(K %*% theSol)))
  return(list(pred = log_pred, alphas = theSol))
}