BIMSA > Seminar on Control Theory and Nonlinear Filtering Universal Approximation Capacity of Bidirectional Recurrent Neural Networks with Noisy Sequential Inputs
Universal Approximation Capacity of Bidirectional Recurrent Neural Networks with Noisy Sequential Inputs
Organizer
Shing Toung Yau
Speaker
Yangtianze Tao
Time
Monday, August 28, 2023 3:00 PM - 3:30 PM
Venue
数学系理科楼A-203
Abstract
In this presentation, we undertake an investigation into the capacity of bidirectional recurrent neural networks (BRNNs) to approximate filtering and smoothing dynamics under the state-space models (SSMs) framework in the presence of noisy sequential inputs. Our analysis initially establishes, under certain reasonable assumptions, that the forward recursions of BRNNs are capable of accurately approximating any filtering dynamics, while the backward recursions of BRNNs satisfactorily approximate the corresponding smoothing dynamics. We present explicit estimation bounds for both filtering and smoothing dynamics and utilize these theoretical results to construct a BRNN-Based smoother, which offers a synthetic resolution to the optimal smoothing problem. By training a BRNN on sequences of observations and their corresponding states produced by computer simulations or actual experiments, we demonstrate that the BRNN-Based smoother can closely approximate the optimal smoother, including approximating the optimal filter as its forward recursion. Finally, we support our theoretical findings through two examples and compare our results numerically against the extended Kalman smoother (EKS) and particle smoother (PS).