Recurrent Neural Networks and Universal Approximation of Bayesian Filters

Understand

We consider the Bayesian optimal filtering problem: i.e.

• estimating some conditional statistics of a latent time-series signal from an observation sequence.
• Classical approaches often rely on the use of assumed or estimated transition and observation models.
• Instead, we formulate a generic recurrent neural network framework and seek to learn directly a recursive mapping from observational inputs to the desired estimator statistics.