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.