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Example of a naive Bayes classifier depicted as a Bayesian Network. In statistics, naive Bayes classifiers are a family of linear "probabilistic classifiers" which assumes that the features are conditionally independent, given the target class. The strength (naivety) of this assumption is what gives the classifier its name.
Standard examples of each, all of which are linear classifiers, are: generative classifiers: naive Bayes classifier and; linear discriminant analysis; discriminative model: logistic regression; In application to classification, one wishes to go from an observation x to a label y (or probability distribution on labels).
Automatically learning the graph structure of a Bayesian network (BN) is a challenge pursued within machine learning. The basic idea goes back to a recovery algorithm developed by Rebane and Pearl [ 7 ] and rests on the distinction between the three possible patterns allowed in a 3-node DAG:
Classic machine learning models like hidden Markov models, neural networks and newer models such as variable-order Markov models can be considered special cases of Bayesian networks. One of the simplest Bayesian Networks is the Naive Bayes classifier .
Bayesian inference (/ ˈ b eɪ z i ə n / BAY-zee-ən or / ˈ b eɪ ʒ ən / BAY-zhən) [1] is a method of statistical inference in which Bayes' theorem is used to calculate a probability of a hypothesis, given prior evidence, and update it as more information becomes available.
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.
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:
Formally, an "ordinary" classifier is some rule, or function, that assigns to a sample x a class label ŷ: ^ = The samples come from some set X (e.g., the set of all documents, or the set of all images), while the class labels form a finite set Y defined prior to training.