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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.
In numerous publications on Bayesian experimental design, it is (often implicitly) assumed that all posterior probabilities will be approximately normal. This allows for the expected utility to be calculated using linear theory, averaging over the space of model parameters. [2]
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 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 .
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 f ϕ ∗ {\displaystyle f_{\phi }^{*}} by directly minimizing the expected risk and without ...
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.
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.
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: