Conformal Prediction Under Generalized Covariate Shift with Posterior Drift

TL;DR

This paper introduces a weighted conformal prediction method for transfer learning under a generalized covariate shift with posterior drift, providing coverage guarantees and demonstrating favorable theoretical and empirical results.

Contribution

It proposes a novel weighted conformal classifier for transfer learning under a new distributional assumption, ensuring coverage in the target domain.

Findings

Provides coverage guarantees in the target domain

Demonstrates asymptotic properties theoretically

Shows effectiveness through numerical studies

Abstract

In many real applications of statistical learning, collecting sufficiently many training data is often expensive, time-consuming, or even unrealistic. In this case, a transfer learning approach, which aims to leverage knowledge from a related source domain to improve the learning performance in the target domain, is more beneficial. There have been many transfer learning methods developed under various distributional assumptions. In this article, we study a particular type of classification problem, called conformal prediction, under a new distributional assumption for transfer learning. Classifiers under the conformal prediction framework predict a set of plausible labels instead of one single label for each data instance, affording a more cautious and safer decision. We consider a generalization of the \textit{covariate shift with posterior drift} setting for transfer learning. Under this setting, we propose a weighted conformal classifier that leverages both the source and target samples, with a coverage guarantee in the target domain. Theoretical studies demonstrate favorable asymptotic properties. Numerical studies further illustrate the usefulness of the proposed method.