A Unified Theory of Conditional Coverage in Conformal Prediction with Applications

2026-05-12

AI Summary

This work addresses the limitations of existing conformal prediction methods, which typically guarantee only marginal coverage and struggle to ensure conditional coverage for heterogeneous test points or subpopulations, while lacking a unified theoretical framework to analyze their asymptotic validity, compare approaches, or extend them to structured data. The paper proposes the first unified theoretical framework tailored for conditional coverage, deriving non-asymptotic bounds on conditional miscoverage via pointwise and Lₚ paths. It systematically characterizes the sources of error underlying asymptotic conditional validity and provides a coherent interpretation of existing methods. Built upon a weighted symmetry formulation, the framework facilitates conditional coverage–oriented model selection, localization under covariate shift, and natural extensions to structured data. Numerical experiments corroborate the theoretical findings, establishing a comparable, extensible, and practically informative paradigm for conditional coverage.

Abstract

Conformal prediction provides finite-sample marginal validity, but many applications require coverage that adapts to heterogeneous test points or subpopulations. Existing methods for conditional coverage are largely analyzed case by case, leaving limited general theory for how asymptotic conditional validity arises, how different procedures should be compared, and how such guarantees extend to structured data. We develop a unified framework and theory for conformal methods targeting conditional coverage. Within this framework, we derive non-asymptotic bounds for conditional miscoverage through two complementary routes: a pointwise route for direct score control and an $L_p$ route for quantile-centered methods. The theory clarifies the error sources governing asymptotic conditional validity, yields a common interpretation of existing methods, and supports applications and extensions to conditional-coverage-oriented model selection, localization under covariate shift, structured-data settings through a weighted symmetry-based formulation and more. Numerical results support the theoretical conclusions.

Problem

• conditional coverage
• conformal prediction
• asymptotic validity
• structured data
• heterogeneous subpopulations

Innovation

• conditional coverage
• conformal prediction
• unified framework
• non-asymptotic bounds
• structured data