时 间：2025年10月16 日（周四）9：30 – 11：00
线 上：腾讯会议ID: 562-254-965，密码: 0831
报告人：王雄 中山大学副教授
主持人：徐方军 华东师范大学教授
摘 要：
Modeling multi-agent systems on networks is a fundamental challenge in a wide variety of disciplines. We jointly infer the weight matrix of the network and the interaction kernel, which determine respectively which agents interact with which others and the rules of such interactions from data consisting of multiple trajectories. The estimator we propose leads naturally to a non-convex optimization problem, and we investigate two approaches for its solution: one is based on the alternating least squares (ALS) algorithm; another is based on a new algorithm named operator regression with alternating least squares (ORALS). Both algorithms are scalable to large ensembles of data trajectories. We establish coercivity conditions guaranteeing identifiability and well-posedness. The ALS algorithm appears statistically efficient and robust even in the small data regime but lacks performance and convergence guarantees. The ORALS estimator is consistent and asymptotically normal under a coercivity condition. We conduct several numerical experiments ranging from Kuramoto particle systems on networks to opinion dynamics in leader-follower models.
报告人简介：
王雄，中山大学副教授，主要研究方向为概率论与数理统计，研究兴趣涵盖随机微分方程及其在机器学习中的应用，特别关注随机偏微分方程（SPDEs）解的长时间行为以及交互粒子系统相关的机器学习问题，并探索其在数据驱动建模中的理论基础与算法设计。近年来，在高斯噪声驱动的SPDEs研究中，围绕解的适定性、间断性(intermittency)现象与均方稳定性等理论问题取得了一系列进展；在交互粒子系统的研究中，结合统计与机器学习方法，系统地研究了相关的非参数推断。相关成果已发表于 Annales de l’Institut Henri Poincaré (B)、Bernoulli、Journal of Machine Learning Research 等国际知名概率与机器学习期刊。