BIMSA > Seminar on Control Theory and Nonlinear Filtering Bidirectional Recurrent Neural Networks Are Universal Smoothers
Bidirectional Recurrent Neural Networks Are Universal Smoothers
Organizer
Shing Toung Yau
Speaker
Yangtianze Tao
Time
Tuesday, November 15, 2022 8:30 PM - 9:00 PM
Venue
Online
Abstract
In this talk, we present the investigation of the approximation capability of bidirectional recurrent neural networks (BRNNs) with stochastic inputs under the state-space models (SSMs) framework. More specifically, under some natural assumptions, we prove that any filtering dynamics can be well-approximated by the forward recursions of BRNNs while the corresponding smoothing dynamics will also be well-approximated by the backward recursions of the BRNNs. Moreover, the estimation bounds are given for both filtering and smoothing dynamics. In addition, as an important application of this result, we construct a BRNN-based smoother which is a synthetic approach to solve the optimal smoothing problem. The realizations, i.e., the sequences of observations and their corresponding states, which are generated by either computer simulation or actual experiments, are synthesized into a smoother by training a BRNN. And we prove that it can well-approximate optimal smoother which include approximating the optimal filter as its forward recursion. At last, our main results are verified in two examples compared with the classical Kalman smoother (KS) and the particle smoother (PS).