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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.
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 : {,, …,}, with the interpretation that C classifies the point x to the class C(x).
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.
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.
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
The softmax function is used in various multiclass classification methods, such as multinomial logistic regression (also known as softmax regression), [2]: 206–209 [6] multiclass linear discriminant analysis, naive Bayes classifiers, and artificial neural networks. [7]
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 training example of SVM with kernel given by φ((a, b)) = (a, b, a 2 + b 2) Suppose now that we would like to learn a nonlinear classification rule which corresponds to a linear classification rule for the transformed data points ().