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In [[machine learning]], a '''probabilistic classifier''' is a [[statistical classification|classifier]] that is able to predict, given a sample input, a [[probability distribution]] over a [[Set (mathematics)|set]] of classes, rather than only outputting the most likely class that the sample should belong to. Probabilistic classifiers provide classification with a degree of certainty, which can be useful in its own right,<ref>{{cite book |first1=Trevor |last1=Hastie |first2=Robert |last2=Tibshirani |first3=Jerome |last3=Friedman |year=2009 |title=The Elements of Statistical Learning |url=http://statweb.stanford.edu/~tibs/ElemStatLearn/ |page=348 |quote=[I]n [[data mining]] applications the interest is often more in the class probabilities <math>p_\ell(x), \ell = 1, \dots, K</math> themselves, rather than in performing a class assignment.}}</ref> or when combining classifiers into [[ensemble classifier|ensembles]].
Formally, an "ordinary" classifier is some rule, or [[function (mathematics)|function]], that assigns to a sample {{mvar|x}} a class label {{mvar|ŷ}}:
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