报告题目：Knowledge Transfer across Multiple Principal Component Analysis Studies

摘 要：Transfer learning has aroused great interest in the statistical community. In this article, we focus on knowledge transfer for unsupervised learning tasks in contrast to the supervised learning tasks in the literature. Given the transferable source populations, we propose a two-step transfer learning algorithm to extract useful information from multiple source principal component analysis (PCA) studies, thereby enhancing estimation accuracy for the target PCA task. In the first step, we integrate the shared subspace information across multiple studies by a proposed method named as Grassmannian barycenter, instead of directly performing PCA on the pooled dataset. The proposed Grassmannian barycenter method enjoys robustness and computational advantages in more general cases. Then the resulting estimator for the shared subspace from the first step is further utilized to estimate the target private subspace in the second step. Our theoretical analysis credits the gain of knowledge transfer between PCA studies to the enlarged eigenvalue gaps of the population covariance matrices, which is different from the existing supervised transfer learning tasks where sparsity of the parameters plays the central role. When the set of informative sources is unknown, we endow our algorithm with the capability of useful dataset selection and solve a rectified optimization problem on the Grassmann manifold, which in turn leads to a computationally friendly rectified Grassmannian K-means procedure. In the end, extensive numerical simulation results and a real data case concerning activity recognition are reported to support our theoretical claims and to illustrate the empirical usefulness of the proposed transfer learning methods.

报告时间：2024年10月12日下午2:30--3:30

报告地点：统计与数据科学学院109会议室

主办单位：统计与数据科学学院

专家简介：何勇，山东大学金融研究院，教授, 博士生导师，山东大学齐鲁青年学者, 山东省泰山学者青年专家，山东省高等学校“金融科技数学理论”青年创新团队负责人; 山东大学学士（2012），复旦大学博士（2017），师从张新生教授；从事金融计量统计、数理统计以及机器学习等方面的研究，在国际统计学、计量经济学权威期刊Annals of Statistics，Journal of Econometrics, Journal of Business and Economic Statistics, Biometrics（封面文章）, Biostatistics等发表研究论文30余篇；现主持国家自然科学基金面上项目。获第一届统计科学技术进步奖一等奖（第二位），担任美国数学评论评论员、中国现场统计研究会生存分析分会副理事长、中国现场统计研究会机器学习分会常务理事及JASA, JRSSB, AOS, JOE, JBES, Biometrics等国际学术期刊匿名审稿人。