# Confidence Predictor

A *confidence predictor* is essentially a prediction algorithm producing prediction regions. In the context of conformal prediction, we assume that Reality outputs successive pairs

called *observations*. The *objects* are elements of a measurable space and the *labels* are elements of a measurable space .

We call the *observation space*, the *significance level*, and the complimentary value the *confidence level*.

A *confidence predictor* is a measurable function ( is a set of all subsets of ) that satisfies

for all significance levels , all positive integers , and all *incomplete data sequences* . Thus, a confidence predictor is an algorithm that given an incomplete data sequence and (the *significance level*), outputs a subset of (the *prediction region*) so that the condition above is satisfied.