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In the statistics literature, naive Bayes models are known under a variety of names, including simple Bayes and independence Bayes. [3] All these names reference the use of Bayes' theorem in the classifier's decision rule, but naive Bayes is not (necessarily) a Bayesian method.
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 ).
Formally, an "ordinary" classifier is some rule, or function, that assigns to a sample x a class label ŷ: y ^ = f ( x ) {\displaystyle {\hat {y}}=f(x)} 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.
Bayes' theorem applied to an event space generated by continuous random variables X and Y with known probability distributions. There exists an instance of Bayes' theorem for each point in the domain. In practice, these instances might be parametrized by writing the specified probability densities as a function of x and y.
Download as PDF; Printable version; In other projects ... A plug-in rule uses an estimate of the posterior probability ... Naive Bayes classifier; References
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.
Bayes' theorem describes the conditional probability of an event based on data as well as prior information or beliefs about the event or conditions related to the event. [3] [4] For example, in Bayesian inference, Bayes' theorem can be used to estimate the parameters of a probability distribution or statistical model. Since Bayesian statistics ...
A loss function is said to be classification-calibrated or Bayes consistent if its optimal is such that / = (()) and is thus optimal under the Bayes decision rule. A Bayes consistent loss function allows us to find the Bayes optimal decision function by directly minimizing the expected risk and without having to explicitly model the ...