报告主题：Data-driven nonparametric probabilistic modeling of dynamical systems
报告人：蒋诗晓 博士后 （The Pennsylvania State University）
报告时间：2019年7月3日（周三）13:30
报告地点：校本部G507
邀请人：赖耕
报告摘要：In this talk, I will introduce you a manifold learning tool (diffusion maps algorithm) and a representation theory based on Reproducing Kernel Hilbert Spaces (RKHS). Then I will apply them to the two application problems, Bayesian inference and modeling of missing dynamics. For Bayesian inference, we consider a surrogate modeling approach using a data-driven nonparametric likelihood function constructed on a manifold on which the data lie. For the other application problem, we consider modeling missing dynamics with a non-Markovian transition density, constructed using the theory of kernel embedding of conditional distributions on appropriate RKHS. Depending on the choice of the basis functions, the resulting closure from this nonparametric modeling formulation is in the form of parametric models. This suggests that the successes of various parametric modeling approaches that were proposed in various domain of applications can be understood through the RKHS representations.

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