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Abstractly, naive Bayes is a conditional probability model: it assigns probabilities (, …,) for each of the K possible outcomes or classes given a problem instance to be classified, represented by a vector = (, …,) encoding some n features (independent variables).
In statistical classification, the Bayes classifier is the classifier having the smallest probability of misclassification of all classifiers using the same set of features. [ 1 ] Definition
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.
Naive Bayes is a successful classifier based upon the principle of maximum a posteriori (MAP). This approach is naturally extensible to the case of having more than two classes, and was shown to perform well in spite of the underlying simplifying assumption of conditional independence .
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A generative model takes the joint probability (,), where is the input and is the label, and predicts the most possible known label ~ for the unknown variable ~ using Bayes' theorem. [ 3 ] Discriminative models, as opposed to generative models , do not allow one to generate samples from the joint distribution of observed and target variables.
In computer science and statistics, Bayesian classifier may refer to: any classifier based on Bayesian probability; a Bayes classifier, one that always chooses the class of highest posterior probability in case this posterior distribution is modelled by assuming the observables are independent, it is a naive Bayes classifier
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.