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General Formula for Prediction via Maximum Probability

The fundamental principle for making a prediction in many machine learning models is to select the output that has the highest probability given an input. This is formally expressed as: y^=argmaxyYPr(yx)\hat{y} = \underset{y \in Y}{\arg\max}\, \text{Pr}(y|x) In this formula, xx is the input, YY is the set of all possible outputs, yy is a candidate output from that set, and y^\hat{y} is the final predicted output. The prediction y^\hat{y} is chosen because it maximizes the conditional probability Pr(yx)\text{Pr}(y|x).

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Updated 2026-05-02

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