# Class membership probabilities

Class membership probabilities

In general proplems of classification, class membership probabilities reflect the uncertainty with which a given indivual item can be assigned to any given class. Although statistical classification methods by definition generate such probabilities, applications of classification in machine learning usually supply membership values that do not induce any probabilistic confidence. It is desirable, to transform or re-scale membership values to class membership probabilities, since they are comparable and additionally are more easily applicable for post-processing.

There exist several univariate calibration methods that transform two-class membership values into membership probabilities. A common approach is to apply the logistic regression approach by Platt (1999). Zadrozny and Elkan (2002) supply an alternative method by using isotonic regression.

Multivariate extensions for regularization methods usually[citation needed] use a reduction to binary tasks, followed by univariate calibration and further application of the pairwise coupling algorithm by Hastie and Tibshirani (1998). An alternative method, the Dirichlet calibration, is introduced by Gebel and Weihs (2008).

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