报告时间：2024年7月24日10:00-11:00

报告地点：维格堂319

报告人：Linglong Kong

报告题目：Gaussian Differential Privacy on Riemannian Manifolds

报告摘要：We develop an advanced approach for extending Gaussian Differential Privacy (GDP) to general Riemannian manifolds. The concept of GDP stands out as a prominent privacy definition that strongly warrants extension to manifold settings, due to its central limit properties. By harnessing the power of the renowned Bishop-Gromov theorem in geometric analysis, we propose a Riemannian Gaussian distribution that integrates the Riemannian distance, allowing us to achieve GDP in Riemannian manifolds with bounded Ricci curvature. To the best of our knowledge, this work marks the first instance of extending the GDP framework to accommodate general Riemannian manifolds, encompassing curved spaces, and circumventing the reliance on tangent space summaries. We provide a simple algorithm to evaluate the privacy budget $\mu$ on any onedimensional manifold and introduce a versatile Markov Chain Monte Carlo (MCMC)based algorithm to calculate $\mu$ on any Riemannian manifold with constant curvature. Through simulations on one of the most prevalent manifolds in statistics, the unit sphere $S^d$, we demonstrate the superior utility of our Riemannian Gaussian mechanism in comparison to the previously proposed Riemannian Laplace mechanism for implementing GDP.

报告人简介：Dr. Linglong Kong is a professor in the Department of Mathematical and Statistical Sciences at the University of Alberta. H He holds a Canada Research Chair in Statistical Learning and a Canada CIFAR AI Chair. He is a fellow of American Statistical Association (ASA) and a fellow of the Alberta Machine Intelligence Institute (AMII). His publication record includes more than 100 peer-reviewed articles in top journals such as AOS, JASA and JRSSB as well as top conferences such as NeurIPS, ICML, ICDM, AAAI, and IJCAI. Dr. Kong currently serves as associate editor of the Journal of the American Statistical Association, the Canadian Journal of Statistics, and Statistics and its Interface. Additionally, Dr. Kong is a member of the Executive Committee of the Western North American Region of the International Biometric Society, chair of the ASA Statistical Computing Session program, and chair of the webinar committee. He served as a guest editor of Canadian Journal of Statistics and Statistics and its Interface, associate editor ofInternational Journal of Imaging Systems and Technology, guest associate editor of Frontiers of Neurosciences, chair of the ASA Statistical Imaging Session, and member of the Statistics Society of Canada's Board of Directors. He is interested in the analysis of high-dimensional and neuroimaging data, statistical machine learning, robust statistics and quantile regression, as well as artificial intelligence for smart health.

邀请人：徐礼柏