Weighted Conformal Prediction Provides Adaptive and Valid Mask-Conditional Coverage for General Missing Data Mechanisms

TL;DR

This paper introduces a reweighted conformal prediction method that guarantees valid coverage under various missing data mechanisms by combining imputation and correction, improving prediction interval efficiency.

Contribution

It proposes a novel split conformal prediction framework with reweighting to handle missing data, ensuring marginal and mask-conditional coverage.

Findings

Guarantees marginal coverage under missing data.

Achieves mask-conditional validity for general missing mechanisms.

Reduces prediction interval width compared to existing methods.

Abstract

Conformal prediction (CP) offers a principled framework for uncertainty quantification, but it fails to guarantee coverage when faced with missing covariates. In addressing the heterogeneity induced by various missing patterns, Mask-Conditional Valid (MCV) Coverage has emerged as a more desirable property than Marginal Coverage. In this work, we adapt split CP to handle missing values by proposing a preimpute-mask-then-correct framework that can offer valid coverage. We show that our method provides guaranteed Marginal Coverage and Mask-Conditional Validity for general missing data mechanisms. A key component of our approach is a reweighted conformal prediction procedure that corrects the prediction sets after distributional imputation (multiple imputation) of the calibration dataset, making our method compatible with standard imputation pipelines. We derive two algorithms, and we show that they are approximately marginally valid and MCV. We evaluate them on synthetic and real-world datasets. It reduces significantly the width of prediction intervals w.r.t standard MCV methods, while maintaining the target guarantees.