Probabilistic classifier

In machine learning, a probabilistic classifier is a classifier that is able to predict, given an observation of an input, a probability distribution over a set of classes, rather than only outputting the most likely class that the observation should belong to. Probabilistic classifiers provide classification that 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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