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I understand the meaning and how to deduce a Bayes optimal classifier in binary classification, but I am not sure how to derive this in the context of multinomial classification. Do we use the naive bayes approach?

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It doesn’t have to be naive. Once modeled the joint distribution, Bayes classifier chooses the class with the maximum posterior regardless of number of classes. Two class examples are typically used because it’s easier to analytically calculate the decision boundary.

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