统计与数据科学系系列学术报告之四百六十一期

时间：2024年12月25日（星期三）9:30-10:30

地点：史带楼301室

主持人：复旦大学管理学院统计与数据科学系郁文教授

报告人：Prof. Yi Yu Department of Statistics University of Warwick

题目：Optimal estimation in private distributed functional data analysis

摘要：We systematically investigate the preservation of differential privacy in functional data analysis, beginning with functional mean estimation and extending to varying coefficient model estimation. Our work introduces a distributed learning framework involving multiple servers, each responsible for collecting several sparsely observed functions. This hierarchical setup introduces a mixed notion of privacy. Within each function, user-level differential privacy is applied to m discrete observations. At the server level, central differential privacy is deployed to account for the centralized nature of data collection. Across servers, only private information is exchanged, adhering to federated differential privacy constraints. To address this complex hierarchy, we employ minimax theory to reveal several fundamental phenomena: from sparse to dense functional data analysis, from user- level to central and federated differential privacy costs, and the intricate interplay between different regimes of functional data analysis and privacy preservation. To the best of our knowledge, this is the first study to rigorously examine functional data estimation under multiple privacy constraints. Our theoretical findings are complemented by efficient private algorithms and extensive numerical evidence, providing a comprehensive exploration of this challenging problem. The paper is available at: arXiv:2412.06582

个人简介：Professor Yi Yu was previously a Reader (2021-23) and an Associate Professor (2019-21) in the University of Warwick, a Lecturer (2017-19) in the University of Bristol, a postdoc (2013-16) of Professor Richard Samworth and a graduate student (2009-13) of Professor Zhiliang Ying. Professor Yi Yu obtained her academic degrees from Fudan University (Ph.D. in Mathematical Statistics, June 2013 and B.Sc. in Mathematics, June 2009). She is a recipient of the Philip Leverhulme Prize in 2023.