Building Machine Learning Systems with Python - Richert, Coelho

Using Naive Bayes to classify
Given a new tweet, the only part left is to simply calculate the probabilities:
Chapter 6
We also need to choose the class having the higher probability. As for both
classes the denominator, , is the same, so we can simply ignore it without
changing the winner class.
Note, however, that we don't calculate any real probabilities any more. Instead,
we are estimating which class is more likely given the evidence. This is another
reason why Naive Bayes is so robust: it is not so much interested in the real
probabilities, but only in the information which class is more likely to. In short,
we can write it as follows:
Here we are calculating the part after argmax for all classes of C ("pos" and "neg"
in our case) and returning the class that results in the highest value.
But for the following example, let us stick to real probabilities and do some
calculations to see how Naive Bayes works. For the sake of simplicity, we will
assume that Twitter allows only for the two words mentioned earlier, awesome
and crazy, and that we had already manually classified a handful of tweets:
Tweet
awesome
awesome
awesome crazy
crazy
crazy
crazy
Class
Positive
Positive
Positive
Positive
Negative
Negative
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