题    目：Sampling Strategies in Sparse Bayesian Inference

主讲人：Yiqiu Dong 副教授

单    位：丹麦科技大学

时    间：2025年3月28日 14:00

地    点：郑州校区九章学堂南楼C座203教室

摘    要：Abstract: Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization. Although the solutions to many such regularized inverse problems can be considered as points of maximum probability of well-chosen posterior distributions, samples from these distributions are generally not sparse. In this talk, we present a sampling strategy for an implicitly defined probability distribution that combines the effects of sparsity imposing regularization with Gaussian distributions. It extends the randomize-then-optimize (RTO) method to sampling from implicitly described continuous probability distributions. We study the properties of these regularized distributions, and compare the proposed method with Langevin-based methods, which are often used for sampling high-dimensional densities.

简    介：Yiqiu Dong received the B.Sc. degree in mathematics from Yantai University, Yantai, China, in 2002 and the Ph.D. degree in mathematics from Peking University under the supervision by Prof. Shufang Xu and Prof. Raymond Chan (Lingnan University, Hong Kong), Beijing, China, in 2007. She is currently associate professor in the Technical University of Denmark. Her research areas include inverse problem and variational methods, uncertianty quantification, mathematical imaging and optimization methods.（邀请人: 庞志峰）