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While naive Bayes often fails to produce a good estimate for the correct class probabilities, [16] this may not be a requirement for many applications. For example, the naive Bayes classifier will make the correct MAP decision rule classification so long as the correct class is predicted as more probable than any other class.
Naive Bayes spam filtering is a baseline technique for dealing with spam that can tailor itself to the email needs of individual users and give low false positive spam detection rates that are generally acceptable to users. It is one of the oldest ways of doing spam filtering, with roots in the 1990s.
A classifier is a rule that assigns to an observation X=x a guess or estimate of what the unobserved label Y=r actually was. In theoretical terms, a classifier is a measurable function C : R d → { 1 , 2 , … , K } {\displaystyle C:\mathbb {R} ^{d}\to \{1,2,\dots ,K\}} , with the interpretation that C classifies the point x to the class C ( x ).
Bayes' theorem is named after the Reverend Thomas Bayes (/ b eɪ z /), also a statistician and philosopher.Bayes used conditional probability to provide an algorithm (his Proposition 9) that uses evidence to calculate limits on an unknown parameter.
It can be drastically simplified by assuming that the probability of appearance of a word knowing the nature of the text (spam or not) is independent of the appearance of the other words. This is the naive Bayes assumption and this makes this spam filter a naive Bayes model. For instance, the programmer can assume that:
A plug-in rule uses an estimate of the posterior probability to form a classification rule. Given an estimate ~, the ... Naive Bayes classifier; References
Some classification models, such as naive Bayes, logistic regression and multilayer perceptrons (when trained under an appropriate loss function) are naturally probabilistic. Other models such as support vector machines are not, but methods exist to turn them into probabilistic classifiers.
Examples of such algorithms include: Linear Discriminant Analysis (LDA)—assumes Gaussian conditional density models; Naive Bayes classifier with multinomial or multivariate Bernoulli event models. The second set of methods includes discriminative models, which attempt to maximize the quality of the output on a training set.