Conformal Prediction Regions are Imprecise Highest Density Regions

Recently, Cella and Martin proved how, under an assumption called consonance, a credal set (i.e. a closed and convex set of probabilities) can be derived from the conformal transducer associated with transductive conformal prediction. We show that the Imprecise Highest Density Region (IHDR) associated with such a credal set corresponds to the classical Conformal Prediction Region. In proving this result, we establish a new relationship between Conformal Prediction and Imprecise Probability (IP) theories, via the IP concept of a cloud. A byproduct of our presentation is the discovery that consonant plausibility functions are monoid homomorphisms, a new algebraic property of an IP tool.