报告题目：Stein Variational Gradient Descent for Functions
报告人：贾骏雄 教授
邀请人：姚青云
报告时间：2023年10月24日（周二）下午15:00-16:00
报告地址：腾讯会议（会议号：918-684-428）
报告摘要：We propose an infinite-dimensional version of the Stein variational gradient descent (iSVGD) method for solving Bayesian inverse problems. The method can generate approximate samples from posteriors efficiently. Based on the concepts of operator-valued kernels and vector-valued reproducing kernel Hilbert spaces, a rigorous definition is given for the infinite-dimensional objects, e.g., the Stein operator, which are proved to be the limit of finite-dimensional ones. Moreover, a more efficient iSVGD with preconditioning operators is constructed by generalizing the change of variables formula and introducing a regularity parameter. The proposed algorithms are applied to an inverse problem of the steady state Darcy flow equation. Numerical results confirm our theoretical findings and demonstrate the potential applications of the proposed approach in the posterior sampling of large-scale nonlinear statistical inverse problems.
报告人简介：贾骏雄，西安交通大学数学与统计学院教授。主要从事数学物理反问题数学理论与计算方法的研究，特别是反问题的贝叶斯推断理论与机器学习方法。至今在Inverse Problems、J. Mach. Learn. Res.、SIAM系列、Math. Comp. 、J. Funct. Anal. 等权威期刊共发表学术论文三十余篇，2017年获得陕西省优秀博士学位论文，2023年获得国家优秀青年科学基金资助，共主持国家自然科学基金项目四项。
数学与统计学院
2023年10月23日
