题 目：SOFARI: High-Dimensional Manifold-Based Inference

主讲人：郑泽敏 教授、博士生导师

时  间：2025年5月24日9:00

地  点：段家滩校区博源楼101

主讲人简介：

郑泽敏，现为中国科学技术大学管理学院教授、统计与金融系主任、博士生导师，其研究方向是高维统计推断和大数据问题。郑泽敏在横跨这一领域的若干关键研究课题上取得了富有创造性的研究成果，发表在国内外权威期刊上，其中包括Journal of the Royal Statistical Society: Series B（JRSSB）、Annals of Statistics（AOS）、Operations Research（OR）、Journal of Machine Learning Research（JMLR）、Journal of Business & Economic Statistics （JBES）等国际统计学、机器学习、计量经济学及管理优化等领域的顶级期刊。他曾获美国数理统计协会颁发的科研新人奖、南加州大学授予的优秀科研奖和中国科大海外校友基金会青年教师事业奖,并入选中组部青年创新人才计划以及福布斯中国U30(30位30岁以下)精英榜。

内容简介：

Multi-task learning is a widely used technique for harnessing information from various tasks. Recently, the sparse orthogonal factor regression (SOFAR) framework, based on the sparse singular value decomposition (SVD) within the coefficient matrix, was introduced for interpretable multi-task learning, enabling the discovery of meaningful latent feature-response association networks across different layers. However, conducting precise inference on the latent factor matrices has remained challenging due to the orthogonality constraints inherited from the sparse SVD constraints. In this paper, we suggest a novel approach called the high-dimensional manifold-based SOFAR inference (SOFARI), drawing on the Neyman near-orthogonality inference while incorporating the Stiefel manifold structure imposed by the SVD constraints. By leveraging the underlying Stiefel manifold structure that is crucial to enabling inference, SOFARI provides easy-to-use bias-corrected estimators for both latent left factor vectors and singular values, for which we show to enjoy the asymptotic mean-zero normal distributions with estimable variances. We introduce two SOFARI variants to handle strongly and weakly orthogonal latent factors, where the latter covers a broader range of applications. We illustrate the effectiveness of SOFARI and justify our theoretical results through simulation examples and a real data application in economic forecasting.