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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
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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 ...
The Bayes optimal classifier is a classification technique. It is an ensemble of all the hypotheses in the hypothesis space. On average, no other ensemble can outperform it. [18] The Naive Bayes classifier is a version of this that assumes that the data is conditionally independent on the class and makes the computation more feasible. Each ...
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.
This optimal decision, a * is known as the Bayes (decision) Rule - it minimises the average loss over all possible states of nature θ, over all possible (probability-weighted) data outcomes. One advantage of the Bayesian approach is to that one need only choose the optimal action under the actual observed data to obtain a uniformly optimal one ...
A Bayes estimator derived through the empirical Bayes method is called an empirical Bayes estimator. Empirical Bayes methods enable the use of auxiliary empirical data, from observations of related parameters, in the development of a Bayes estimator. This is done under the assumption that the estimated parameters are obtained from a common prior.
To evaluate a classifier, one compares its output to another reference classification – ideally a perfect classification, but in practice the output of another gold standard test – and cross tabulates the data into a 2×2 contingency table, comparing the two classifications.