An Information Theoretic Perspective on Conformal Prediction

TL;DR

This paper connects conformal prediction with information theory to improve uncertainty estimation, enabling principled training objectives and incorporation of side information, validated through empirical experiments.

Contribution

It introduces a theoretical framework linking conformal prediction to information theory and develops new training methods and mechanisms for side information integration.

Findings

Lower average prediction set size in experiments

Effective incorporation of side information

Enhanced training objectives for conformal prediction

Abstract

Conformal Prediction (CP) is a distribution-free uncertainty estimation framework that constructs prediction sets guaranteed to contain the true answer with a user-specified probability. Intuitively, the size of the prediction set encodes a general notion of uncertainty, with larger sets associated with higher degrees of uncertainty. In this work, we leverage information theory to connect conformal prediction to other notions of uncertainty. More precisely, we prove three different ways to upper bound the intrinsic uncertainty, as described by the conditional entropy of the target variable given the inputs, by combining CP with information theoretical inequalities. Moreover, we demonstrate two direct and useful applications of such connection between conformal prediction and information theory: (i) more principled and effective conformal training objectives that generalize previous approaches and enable end-to-end training of machine learning models from scratch, and (ii) a natural mechanism to incorporate side information into conformal prediction. We empirically validate both applications in centralized and federated learning settings, showing our theoretical results translate to lower inefficiency (average prediction set size) for popular CP methods.