Game Of Prediction
A game of prediction is a triple , where is an outcome space, is a decision space, and is the loss function. Important special cases are those of:
- point predictions, where ;
- probability predictions, where is the set of all probability measures on ; if is finite, the usual loss function is the log loss;
- region predictions, where is the set of all subsets of ; the usual loss function is
The case of region predictions (in particular, interval predictions) is the main object of study in conformal prediction but has never been studied in competitive on-line prediction. This is stated as open problem in the article competitive on-line interval prediction.