报告人 ：钱洪江（美国康涅狄格大学）

时间：2023年04月27日 14:30--

地址：手机买球赛正规软件LD202

摘要：In this talk, I will first talk about the filtering algorithm for the case of degenerate observation noise using stochastic approximation approach. And an example will be presented to demonstrate the algorithm. Then I will mainly introduce a new class of deep neural network-based numerical algorithms for nonlinear filtering named deep filter.It presents a computationally feasible procedure for regimes-witching diffusions. In lieu of the traditional conditional-distributionbased filtering that suffers from curse of dimensionality, we convert it to a problem in a finite dimensional setting to approximate the optimal weights of a neural network. Then we construct a stochastic gradient-type procedure to approximate these weight parameters, and develop another recursion for adaptively approximating the optimal learning rate. We show the convergence of the continuous time interpolated learning rate process using stochastic averaging and martingale methods. An error bound will be obtained for parameters of the neural network. Several examples will be presented to show the robustness of the algorithm. This is based on joint work with Prof. George Yin and Prof. Qing Zhang.

简介：钱洪江，博士生，就读于美国康涅狄格大学数学系。本科毕业于华中科技大学，研究兴趣是应用概率，随机逼近和大偏差理论。

邀请人：李曼曼

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