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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
In 2004, an analysis of the Bayesian classification problem showed that there are sound theoretical reasons for the apparently implausible efficacy of naive Bayes classifiers. [4] Still, a comprehensive comparison with other classification algorithms in 2006 showed that Bayes classification is outperformed by other approaches, such as boosted ...
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The bayes classifier is the classifier which assigns classes optimally based on the known attributes (i.e. features or regressors) of the elements to be classified. A special kind of classification rule is binary classification, for problems in which there are only two classes.
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 ...
Early work on statistical classification was undertaken by Fisher, [1] [2] in the context of two-group problems, leading to Fisher's linear discriminant function as the rule for assigning a group to a new observation. [3] This early work assumed that data-values within each of the two groups had a multivariate normal distribution.
Since Bayesian statistics treats probability as a degree of belief, Bayes' theorem can directly assign a probability distribution that quantifies the belief to the parameter or set of parameters. [2] [3] Bayesian statistics is named after Thomas Bayes, who formulated a specific case of Bayes' theorem in a paper published in 1763.
Statistical classification is a problem studied in machine learning in which the classification is performed on the basis of a classification rule. It is a type of supervised learning, a method of machine learning where the categories are predefined, and is used to categorize new probabilistic observations into said categories. When there are ...