A WGAN Based Method for Stochastic Filtering

Abstract

The problem of extracting information about a state from incomplete noisy measurement is knowns as a ”filtration problem” in the field of stochastic processes. In this thesis the information extracted corresponds to an estimate of the posterior conditional distribution of a stochastic process. Recent development in generative adversarial networks allows for such filtering problems to be solved using a network class called the WGAN. In this thesis a method of implementing the WGAN for filtration is investigated. The method is tested for a linear SDE scaled in dimensions and on a non-linear SDE of singular dimension. both examples were observed linearly with additive Gaussian noise. The method was benchmarked against filtering methods not based on machine learning. In summary it can be stated the the results indicated that some merit to the method could be deducted. It was however the result that the method was outperformed by most of its peers. An investigation into where the method could be improved was conducted.