Multi-Source Conformal Inference Under Distribution Shift

TL;DR

This paper develops a distribution-free conformal inference method for multi-source data under distribution shifts, enabling valid prediction intervals while addressing bias, privacy, and heterogeneity issues.

Contribution

It introduces a novel approach to obtain valid prediction intervals in multi-source environments with biased data and distribution shifts, incorporating machine learning and adaptive weighting.

Findings

Method achieves nominal coverage probabilities in synthetic experiments.

Proposed approach improves efficiency by upweighting informative sources.

Application to hospital data demonstrates practical utility.

Abstract

Recent years have experienced increasing utilization of complex machine learning models across multiple sources of data to inform more generalizable decision-making. However, distribution shifts across data sources and privacy concerns related to sharing individual-level data, coupled with a lack of uncertainty quantification from machine learning predictions, make it challenging to achieve valid inferences in multi-source environments. In this paper, we consider the problem of obtaining distribution-free prediction intervals for a target population, leveraging multiple potentially biased data sources. We derive the efficient influence functions for the quantiles of unobserved outcomes in the target and source populations, and show that one can incorporate machine learning prediction algorithms in the estimation of nuisance functions while still achieving parametric rates of convergence to nominal coverage probabilities. Moreover, when conditional outcome invariance is violated, we propose a data-adaptive strategy to upweight informative data sources for efficiency gain and downweight non-informative data sources for bias reduction. We highlight the robustness and efficiency of our proposals for a variety of conformal scores and data-generating mechanisms via extensive synthetic experiments. Hospital length of stay prediction intervals for pediatric patients undergoing a high-risk cardiac surgical procedure between 2016-2022 in the U.S. illustrate the utility of our methodology.