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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
Types of discriminative models include logistic regression (LR), conditional random fields (CRFs), decision trees among many others. Generative model approaches which uses a joint probability distribution instead, include naive Bayes classifiers, Gaussian mixture models, variational autoencoders, generative adversarial networks and others.
Binary probabilistic classifiers are also called binary regression models in statistics. In econometrics, probabilistic classification in general is called discrete choice. Some classification models, such as naive Bayes, logistic regression and multilayer perceptrons (when trained under an appropriate loss function) are
The model is initially fit on a training data set, [3] which is a set of examples used to fit the parameters (e.g. weights of connections between neurons in artificial neural networks) of the model. [4] The model (e.g. a naive Bayes classifier) is trained on the training data set using a supervised learning method, for example using ...
Bayes' theorem is named after Thomas Bayes (/ b eɪ z /), a minister, statistician, and philosopher. Bayes used conditional probability to provide an algorithm (his Proposition 9) that uses evidence to calculate limits on an unknown parameter. His work was published in 1763 as An Essay Towards Solving a Problem in the Doctrine of Chances.
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 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 .