Conformal Prediction Regions are Imprecise Highest Density Regions

TL;DR

This paper reveals that conformal prediction regions are equivalent to Imprecise Highest Density Regions under certain conditions, establishing a new link between conformal prediction and Imprecise Probability theories.

Contribution

It demonstrates the equivalence between conformal prediction regions and Imprecise Highest Density Regions, and uncovers a novel algebraic property of consonant plausibility functions.

Findings

Conformal prediction regions are equivalent to Imprecise Highest Density Regions under consonance.

A new relationship between conformal prediction and Imprecise Probability is established.

Consonant plausibility functions are shown to be monoid homomorphisms.

Abstract

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.