simple.logistic = function(x, y, w, iters=30, l1_penalty=0) {
  d = ncol(x)
  n = nrow(x)
  x_c = colMeans(x)
  x = (x - matrix(rep(x_c, n), nrow=n, byrow = T))
  x_s = sqrt(colMeans(x^2))
  x = (x / matrix(rep(x_s, n), nrow=n, byrow = T))
  beta = rep(0,d)
  p = weighted.mean(y, w = w)
  beta_0 = log(p) - log(1-p)
  for (iter_ in 1:iters) {
    pred = 1 / (1 + exp(-x %*% beta - beta_0))
    weights = w * pred * (1 - pred)
    rw = matrix(rep(weights, d), ncol=d)
    ob = beta
    XTX = t(x) %*% (rw * x)
    XTX = XTX + sum(w) * l1_penalty * diag(1/(abs(beta)+1e-5))
    beta = beta + qr.solve(XTX, t(x) %*% (w * (y - pred)))
    if (mean((beta - ob)^2)<1e-6) {
      break
    }
  }
  obj = list(beta=beta, beta_0=beta_0, x_c = x_c, x_s = x_s)
  class(obj) = "simple.logistic"
  return(obj)
}