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What is naive about Naive Bayes? Have an exam later, and this was a question on the sample paper we received. We haven't found a good clear answer yet, could anyone explain this?

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You need not be embarassed Peddler, you have asked a good question. +1 –  Yavar May 16 '12 at 8:40
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2 Answers

up vote 8 down vote accepted

There's actually a very good example on Wikipedia:

In simple terms, a naive Bayes classifier assumes that the presence (or absence) of a particular feature of a class is unrelated to the presence (or absence) of any other feature, given the class variable. For example, a fruit may be considered to be an apple if it is red, round, and about 4" in diameter. Even if these features depend on each other or upon the existence of the other features, a naive Bayes classifier considers all of these properties to independently contribute to the probability that this fruit is an apple.

Basically, it's "naive" because it makes assumptions that may or may not turn out to be correct.

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I must say, I'm fairly embarrassed I asked this question now! Thanks Laurent! –  Peddler May 16 '12 at 8:36
+1 for statement starting from "Basically, it's "naive"...." –  Yavar May 16 '12 at 8:39
The wikipedia article explains it correctly, but I disagree that "it makes assumptions that may or may not turn out to be correct". With right amount of training data it does a good job of filtering out the irrelevant parameters. The "naive" part is that is does not consider dependence between the parameters.. and hence may have to look at redundant data. –  Chip May 16 '12 at 8:50
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If your data is composed of a feature vector X = {x1, x2, ... x10} and your class labels Y = {y1, y2, .. y5}. Thus, a Bayes classifier identifies the correct class label as the one that maximizes the following formula :

P(y/X) = P(X/y) * P(y) = P(x1,x2, ... x10/ y) * P(y)

So for, it is still not Naive. However, it is hard to calculate P(x1,x2, ... x10/ Y), so we assume the features to be independent, this is what we call the Naive assumption, hence, we end up with the following formula instead

P(y/X) = P(x1/y) * P(x2/y) * ... P(x10/y) * P(y)

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