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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
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 ...
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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 ...
A training data set is a data set of examples used during the learning process and is used to fit the parameters (e.g., weights) of, for example, a classifier. [9] [10]For classification tasks, a supervised learning algorithm looks at the training data set to determine, or learn, the optimal combinations of variables that will generate a good predictive model. [11]
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.
Binary probabilistic classifiers are also called binary regression models in statistics. In econometrics, probabilistic classification in general is called discrete choice. Some classification models, such as naive Bayes, logistic regression and multilayer perceptrons (when trained under an appropriate loss function) are
For two univariate distributions and with the same standard deviation, it is denoted by ′ ('dee-prime'): ′ = | |. In higher dimensions, i.e. with two multivariate distributions with the same variance-covariance matrix , (whose symmetric square-root, the standard deviation matrix, is ), this generalizes to the Mahalanobis distance between the two distributions: