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Treat the
frequencies of classes in each partition as
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probabilities and
compute the entropy.
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This
is a natural measure if we want to maximize the
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log
probability of the correct answer.
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Treat the
frequencies as probabilities and use an
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unprincipled
measure called the Gini index.
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It
was invented by frequentist statisticians and it just
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happens
to work pretty well.
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