Conformalized Regression for Continuous Bounded Outcomes

TL;DR

This paper develops conformal prediction intervals tailored for bounded continuous outcomes using transformation models and beta regression, ensuring valid coverage even under model misspecification.

Contribution

It introduces new non-conformity measures aligned with the models and provides theoretical and empirical validation of the conformal intervals for bounded outcomes.

Findings

Both conformal methods achieve valid finite-sample coverage.

The methods remain valid under model misspecification.

Practical performance demonstrated on real data.

Abstract

Regression problems with bounded continuous outcomes frequently arise in real-world statistical and machine learning applications, such as the analysis of rates and proportions. A central challenge in this setting is predicting a response associated with a new covariate value. Most of the existing statistical and machine learning literature has focused either on point prediction of bounded outcomes or on interval prediction based on asymptotic approximations. We develop conformal prediction intervals for bounded outcomes based on transformation models and beta regression. We introduce tailored non-conformity measures based on residuals that are aligned with the underlying models, and account for the inherent heteroscedasticity in regression settings with bounded outcomes. We present a theoretical result on asymptotic marginal and conditional validity in the context of full conformal prediction, which remains valid under model misspecification. For split conformal prediction, we provide an empirical coverage analysis based on a comprehensive simulation study. The simulation study demonstrates that both methods provide valid finite-sample predictive coverage, including settings with model misspecification. Finally, we demonstrate the practical performance of the proposed conformal prediction intervals on real data and compare them with bootstrap-based alternatives.