Academic Report of School of Mathematical Sciences [2025] No. 149

(Series Report for High-Level University Construction No. 1250)

Title: Distribution-Free Prediction Sets for Regression under Target Shift

Speaker：Professor Yanlin Tang（East China Normal University）

Time：10:20-11:20, Dec.7, 2025

Location：Huixing Building 514, Yuehai Campus, Shenzhen University

Abstract：In real-world applications, the limited availability of labeled outcomes presents significant challenges for statistical inference, due to high collection costs, technical barriers, and other constraints. In this work, we construct efficient conformal prediction sets for new target outcomes by leveraging a source distribution—distinct from the target but related through a distributional shift assumption—that provides abundant labeled data.

When the target data are fully unlabeled, our predictions rely solely on the source distribution; when partial labels are available, they are integrated with the source data to improve efficiency. To address the challenges of data non-exchangeability and distribution non-identifiability, we identify the likelihood ratio by matching the covariate distributions of the source and target domains within a finite B-spline space. To accommodate complex error structures such as asymmetry and multimodality, our method constructs the highest predictive density sets using a novel weight-adjusted conditional density estimator. This estimator models the source conditional density along a quantile process and transforms it—via appropriate weighting adjustments—to approximate the target conditional density. We establish the theoretical properties of the proposed method and evaluate its finite-sample performance through simulation studies and a real-data application to the MIMIC-III clinical database.

Speaker Profile：Yanlin Tang, Professor and Doctoral Supervisor at the School of Statistics, East China Normal University, serves as Chair of the Department of Statistics. He has been selected for the National High-Level Talent Program for Young Professionals and the Shanghai Pujiang Talent Program. His primary research focuses on quantile regression, conformal prediction, and statistical inference for high-dimensional heterogeneous data. He has led multiple projects funded by the National Natural Science Foundation of China and the Shanghai Natural Science Foundation. He serves on the editorial boards of the SCI-indexed journals Statistica Sinica and Journal of the Korean Statistical Society. He has published over 40 papers in journals including Biometrika, JRSSB, PNAS, and Biometrics.

Faculty and students are welcome to attend!

Invited by:  Yan Zhou

School of Mathematical Sciences

December 6, 2025