Conformal Prediction Under Generalized Covariate Shift with Posterior Drift
This work addresses transfer learning challenges for classification tasks where data collection is limited, offering a cautious prediction approach with theoretical guarantees, though it appears incremental as it extends existing settings.
The paper tackles the problem of conformal prediction under a generalized covariate shift with posterior drift setting, proposing a weighted conformal classifier that leverages source and target samples to provide coverage guarantees in the target domain, with theoretical and numerical validation.
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.