= Classification-tree deviance
{title2=$D(t)=-2\sum_kn_{tk}\log(n_{tk}/n_t)$}
Maximizing a node's multinomial likelihood gives class probabilities $\widehat p_{tk}=n_{tk}/n_t$. Twice the negative maximized log-likelihood relative to perfect classification is the displayed deviance, with $0\log0=0$. It equals twice the node size times its <Shannon entropy>. A split is chosen by maximizing $D(t)-D(t_L)-D(t_R)$, and tree deviance is the sum over terminal nodes. The training misclassification count is instead $\sum_t(n_t-\max_kn_{tk})$; the two criteria are different.
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