Conformal Inference For Missing Data under Multiple Robust Learning

TL;DR

This paper introduces a new conformal inference method for missing data under the MAR assumption, combining split conformal calibration with a robust empirical-likelihood reweighting scheme to ensure reliable prediction intervals.

Contribution

It proposes CM--MRL, a novel procedure that achieves robust conformal inference for MAR data by integrating split conformal calibration with multiple empirical-likelihood reweighting.

Findings

Provides asymptotic guarantees for the estimators.

Achieves reliable marginal and conditional coverage.

Demonstrates effectiveness through numerical experiments.

Abstract

We develop a novel approach to tackle the common but challenging problem of conformal inference for missing data in machine learning, focusing on Missing at Random (MAR) data. We propose a new procedure Conformal prediction for Missing data under Multiple Robust Learning (CM--MRL) that combines split conformal calibration with a multiple robust empirical-likelihood (EL) reweighting scheme. The method proceeds via a double calibration by reweighting the complete-case scores by EL so that their distribution matches the full calibration distribution implied by MAR, even when some working models are misspecified. We demonstrate the asymptotic behavior of our estimators through empirical process theory and provide reliable coverage for our prediction intervals, both marginally and conditionally and we further show an interval-length dominance result. We show the effectiveness of the proposed method by several numerical experiments in the presence of missing data.