Need impurity importance and OOB performance for Poisson split rule

[mayer79]

The Poisson split rule is very nice. However, we don't have corresponding

• OOB performance (mean Poisson deviance),
• and correct split gain importance ("impurity").

A formula to get the mean Poisson deviance is:

mean_poisson_deviance <- function(y, pred, weights = rep(1, length(y))) {
  sum(stats::poisson()$dev.resids(y, pred, weights)) / sum(weights)
}

And correspondingly, the split gain:

poisson_split_gain <- function(y, pred, weights = rep(1, length(y))) {
  sum(stats::poisson()$dev.resids(y, pred, weights))
}