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A naive Bayes classifier is a simple probabilistic classifier based on applying Bayes' theorem with strong independence assumptions. A more descriptive term for the underlying probability model would be "independent feature model".

15
votes
Unlike some classifiers, multi-class labeling is trivial with Naive Bayes. For each test example $i$, and each class $k$ you want to find: $$\arg \max_k P(\textrm{class}_k | \textrm{data}_i)$$ In ot …
answered Mar 19 '15 by Matt Krause
2
votes
One common solution is to treat tokens seen less than $n$ times (across all classes) as a special "unknown" or "rare" token. You then use this probability to assign values to legitimately unknown know …
answered Aug 28 '14 by Matt Krause
49
votes
I'm going to run through the whole Naive Bayes process from scratch, since it's not totally clear to me where you're getting hung up. We want to find the probability that a new example belongs to eac …
answered Jan 28 '12 by Matt Krause
2
votes
This is an ugly, ugly solution, but if you're locked into e1071, you can pass the 'raw' option to predict, which will give you the probabilities of each class. You could then "correct" these by divi …
answered Aug 11 '12 by Matt Krause
2
votes
The two metrics measure slightly different things. Naive Bayes tries to learn how to approximate $P(\textrm{class } | \textrm{ data})$ from your training data. To classify new data, the algorithm tak …
answered Jun 23 '15 by Matt Krause
2
votes
This is obviously an interesting (and useful) piece of information to have, and it's been studied extensively under the name "feature selection" (or ranking, etc). There are lots of schemes, many of w …
answered Dec 17 '12 by Matt Krause
7
votes
The third option is right one. In general, it is true that: $$ \log(ab) = \log(a) + \log(b)$$ Plugging in the Naive Bayes equation, you get $$ \log(P(\text{class }_i| \textbf{ data})) \propto \log(P(\ …
answered Jul 25 '15 by Matt Krause
1
vote
Think about your extra information as a new prior: $P(\textrm{Poisonous}) = 0.05$. It should be pretty easy to slot that into Bayes' Rule, no?
answered Apr 20 '13 by Matt Krause
2
votes
As the name suggests, the ideal observer is ... ideal, in that it makes the best possible use of the information available to it and cannot be beat, even by very sophisticated techniques. However, kee …
answered Sep 12 '15 by Matt Krause