Conformal Inference under High-Dimensional Covariate Shifts via Likelihood-Ratio Regularization

TL;DR

This paper introduces LR-QR, a new conformal prediction method that maintains valid coverage under covariate shift in high-dimensional data without explicitly estimating likelihood ratios.

Contribution

The paper proposes the likelihood ratio regularized quantile regression (LR-QR) algorithm, enabling conformal prediction under covariate shift without direct likelihood ratio estimation, suitable for high-dimensional data.

Findings

LR-QR achieves valid coverage in the target domain.

Outperforms existing methods on high-dimensional datasets.

Effective in diverse tasks including image classification and question-answering.

Abstract

We consider the problem of conformal prediction under covariate shift. Given labeled data from a source domain and unlabeled data from a covariate shifted target domain, we seek to construct prediction sets with valid marginal coverage in the target domain. Most existing methods require estimating the unknown likelihood ratio function, which can be prohibitive for high-dimensional data such as images. To address this challenge, we introduce the likelihood ratio regularized quantile regression (LR-QR) algorithm, which combines the pinball loss with a novel choice of regularization in order to construct a threshold function without directly estimating the unknown likelihood ratio. We show that the LR-QR method has coverage at the desired level in the target domain, up to a small error term that we can control. Our proofs draw on a novel analysis of coverage via stability bounds from learning theory. Our experiments demonstrate that the LR-QR algorithm outperforms existing methods on high-dimensional prediction tasks, including a regression task for the Communities and Crime dataset, an image classification task from the WILDS repository, and an LLM question-answering task on the MMLU benchmark.