Conformal Prediction Under Generalized Covariate Shift with Posterior Drift

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.

Conformal Inference of Individual Treatment Effects Using Conditional Density Estimates

In an era where diverse and complex data are increasingly accessible, the precise prediction of individual treatment effects (ITE) becomes crucial across fields such as healthcare, economics, and public policy. Current state-of-the-art approaches, while providing valid prediction intervals through Conformal Quantile Regression (CQR) and related techniques, often yield overly conservative prediction intervals. In this work, we introduce a conformal inference approach to ITE using the conditional density of the outcome given the covariates. We leverage the reference distribution technique to efficiently estimate the conditional densities as the score functions under a two-stage conformal ITE framework. We show that our prediction intervals are not only marginally valid but are narrower than existing methods. Experimental results further validate the usefulness of our method.