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I am currently looking into the multinomial model for Naive Bayes classification, and have come across the following example:

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I think I understand everything, but I have developed the following reasoning I would like confirmed:

For a given class c, and document d consisting of terms t1, t2, ..., tn. Here is how to calculate P(c|d):

  • P(class | doc): (prior[c]) * (prob[t1 in c]) * (prob[t2 in c]) * ... * (prob[tn in c])

  • P (! class | doc): (prior[!c]) * (prob[t1 in !c]) * (prob[t2 in !c]) * ... * (prob[tn in !c])

Is this correct? And thus, is this the reason the power 3 is present in both (3/7) and (2/9), denoting P(Chinese|c) and P(Chinese|!c) together with the fact that 'Chinese' appears three times in d5?

Thank you in advance.

yulai
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