Shape-Adaptive Conditional Calibration for Conformal Prediction via Minimax Optimization

TL;DR

This paper introduces MOPI, a minimax optimization framework for conformal prediction that improves shape adaptivity and conditional coverage, with strong theoretical guarantees and empirical advantages.

Contribution

It proposes a novel minimax formulation for conformal calibration that enhances shape adaptivity and conditional coverage, surpassing prior fixed-set methods.

Findings

MOPI achieves superior shape adaptivity and coverage accuracy.

Theoretical bounds show optimal convergence rates for coverage error.

Empirical results demonstrate more efficient prediction sets on complex distributions.

Abstract

Achieving valid conditional coverage in conformal prediction is challenging due to the theoretical difficulty of satisfying pointwise constraints in finite samples. Building upon the characterization of conditional coverage through marginal moment restrictions, we introduce Minimax Optimization Predictive Inference (MOPI), a framework that generalizes prior work by optimizing over a flexible class of set-valued mappings during the calibration phase, rather than simply calibrating a fixed sublevel set. This minimax formulation effectively circumvents the structural constraints of predefined score functions, achieving superior shape adaptivity while maintaining a principled connection to the minimization of mean squared coverage error. Theoretically, we provide non-asymptotic oracle inequalities and show that the convergence rate of the coverage error attains the optimal order under regular conditions. The MOPI also enables valid inference conditional on sensitive attributes that are available during calibration but unobserved at test time. Empirical results on complex, non-standard conditional distributions demonstrate that MOPI produces more efficient prediction sets than existing baselines.