Analytical solution to Logistic Kernel Ridge Regression in R. Arguments: K = Gram or kernel matrix, y = response, lambda = regularizing coefficient

Logistic_Kernel_Ridge_Regression.R

KRR_logit <- function(K,y, lambda){
  #### Logistic KRR
  # KRR_logit(K,presence)
  N = nrow(K)
  alpha = rep(1/N, N) # initialize alpha parameters
  Kalpha = as.vector(K %*% alpha)
  spec = 1 + exp(-Kalpha)
  pi = 1 / spec
  diagW = pi * (1 - pi)
  e = (y - pi) / diagW
  q = Kalpha + e
  ident.N <- diag(rep(1,N)) # added by me
  theSol = solve(K + lambda * ident.N, q)
  log_pred <- 1 / (1 + exp(-as.vector(K %*% theSol)))
  return(list(pred = log_pred, alphas = theSol))
}