Probabilistic classification

In machine learning, a probabilistic classifier is a classifier that is able to predict, given a sample input, a probability distribution over a 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, or when combining classifiers into ensembles.

Formally, an "ordinary" classifier is some rule, or function, that assigns to a sample x a class label ŷ:

The samples come from some set X (e.g., the set of all documents, or the set of all images), while the class labels form a finite set Y defined prior to training.

Probabilistic classifiers generalize this notion of classifiers: instead of functions, they are conditional distributions ${\displaystyle \Pr(Y\vert X)}$, meaning that for a given ${\displaystyle x\in X}$, they assign probabilities to all ${\displaystyle y\in Y}$ (and these probabilities sum to one). "Hard" classification can then be done using the optimal decision rule

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