Once you have the probabilities of a document in a category
containing a particular word, you need a way to combine the individual
word probabilities to get the probability that an entire document
belongs in a given category. This chapter will consider two different
classification methods. Both of them work in most situations, but they
vary slightly in their level of performance for specific tasks. The
classifier covered in this section is called a *naïve Bayesian
classifier*.

This method is called *naïve* because it
assumes that the probabilities being combined are
*independent* of each other. That is, the probability
of one word in the document being in a specific category is unrelated to
the probability of the other words being in that category. This is
actually a false assumption, since you'll probably find that documents
containing the word "casino" are much more likely to contain the word
"money" than documents about Python programming are.

This means that you can't actually use the probability created by
the naïve Bayesian classifier as the actual probability that a document
belongs in a category, because the assumption of independence makes it
inaccurate. However, you can *compare* the results
for different categories and see which one has the highest probability.
In real life, despite the underlying flawed assumption, this has proven
to be a surprisingly effective method for classifying documents.

To use the naïve Bayesian classifier, ...

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