The Joys of Categorical Conformal Prediction
Journal:
arXiv
Published Date:
Jul 6, 2025
Abstract
Conformal prediction (CP) is an Uncertainty Representation technique that
delivers finite-sample calibrated prediction regions for any underlying Machine
Learning model, yet its status as an Uncertainty Quantification (UQ) tool has
remained conceptually opaque. We adopt a category-theoretic approach to CP --
framing it as a morphism, embedded in a commuting diagram, of two newly-defined
categories -- that brings us three joys. First, we show that -- under minimal
assumptions -- CP is intrinsically a UQ mechanism, that is, its UQ capabilities
are a structural feature of the method. Second, we demonstrate that CP bridges
(and perhaps subsumes) the Bayesian, frequentist, and imprecise probabilistic
approaches to predictive statistical reasoning. Finally, we show that a
conformal prediction region (CPR) is the image of a covariant functor. This
observation is relevant to AI privacy: It implies that privacy noise added
locally does not break coverage.
