报告人：José A. Carrillo 教授（牛津大学）

报告题目：Stein-Log-Sobolev inequalities for the continuous Stein variational gradient descent method

报告摘要： The Stein Variational Gradient Descent method is a variational inference method in statistics that has recently received a lot of attention. The method provides a deterministic approximation of the target distribution, by introducing a nonlocal interaction with a kernel. Despite the significant interest, the exponential rate of convergence for the continuous method has remained an open problem, due to the difficulty of establishing the related so-called Stein-log-Sobolev inequality. Here, we prove that the inequality is satisfied for each space dimension and every kernel whose Fourier transform has a quadratic decay at infinity and is locally bounded away from zero and infinity. Moreover, we construct weak solutions to the related PDE satisfying exponential rate of decay towards the equilibrium. The main novelty in our approach is to interpret the Stein-Fisher information, also called the squared Stein discrepancy, which allows us to employ the Fourier transform. We also provide several examples of kernels for which the Stein-log-Sobolev inequality fails, partially showing the necessity of our assumptions.

报告时间：2025年11月14日（星期五）17:00-18:00（北京时间） 
报告地点：线上 Zoom 会议（会议号：867 8209 3410）

报告人简介： José A. Carrillo 教授是英国牛津大学教授、欧洲科学院院士，2026年AMS会士。Carrillo 教授在偏微分方程、最优输运理论及其应用数学领域享有国际声誉，其研究在理论分析与实际应用方面均具有深远影响。相关成果发表在 Inventiones Mathematicae、Communications on Pure and Applied Mathematics、Journal of the European Mathematical Society、Archive for Rational Mechanics and Analysis 等国际顶级数学期刊上。