null_logLoss <- function(observed) {
n_1 <- sum(observed == 1)
n_0 <- sum(observed == 0)
rate <- mean(observed == 1)
null_logLoss <- -1 * (n_1 * log(rate) + n_0 * log(1 - rate)) / (n_1 + n_0)
return(null_logLoss)
}
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