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 rescale membership values to class membership probabilities, since they are comparable and additionally are more easily applicable for postprocessing.
There exist several univariate calibration methods that transform twoclass membership values into membership probabilities. A common approach is to apply the logistic regression approach by Platt (1999).^{[1]} Zadrozny and Elkan (2002)^{[2]} 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).^{[3]} An alternative method, the Dirichlet calibration, is introduced by Gebel and Weihs (2008).^{[4]}
References
 ^ J. C. Platt, "Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods". In: A. J. Smola, P. Bartlett, B. Schölkopf and D. Schuurmans (eds.), Advances in Large Margin Classiers, 61–74. Cambridge, MIT Press, 1999.
 ^ B. Zadrozny and C. Elkan, Transforming classifier scores into accurate multiclass probability estimates. In: Proceedings of the Eighth International Conference on Knowledge Discovery and Data Mining , 694699, Edmonton, ACM Press, 2002.
 ^ T. Hastie and R. Tibshirani, "Classification by pairwise coupling". In: M. I. Jordan, M. J. Kearns and S. A. Solla (eds.), Advances in Neural Information Processing Systems, volume 10, Cambridge, MIT Press, 1998.doi:10.1.1.46.6032
 ^ M. Gebel and C. Weihs, "Calibrating Margin–Based Classifier Scores into Polychotomous Assessment Probabilities". In: C. Preisach, H. Burkhardt, L. SchmidtThieme and R. Decker (Eds.), Data Analysis, Machine Learning and Applications, Springer, 29–36, 2008
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