Shape-Adaptive Conditional Calibration for Conformal Prediction via Minimax Optimization

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Bao, Yajie, Zhang, Chuchen, Wang, Zhaojun, Ren, Haojie, Zou, Changliang
Format: Preprint
Published: 2026
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866918495334170624
author Bao, Yajie
Zhang, Chuchen
Wang, Zhaojun
Ren, Haojie
Zou, Changliang
author_facet Bao, Yajie
Zhang, Chuchen
Wang, Zhaojun
Ren, Haojie
Zou, Changliang
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2603_23374
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Shape-Adaptive Conditional Calibration for Conformal Prediction via Minimax Optimization
Bao, Yajie
Zhang, Chuchen
Wang, Zhaojun
Ren, Haojie
Zou, Changliang
Methodology
Machine Learning
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.
title Shape-Adaptive Conditional Calibration for Conformal Prediction via Minimax Optimization
topic Methodology
Machine Learning
url https://arxiv.org/abs/2603.23374