ABSTRACT

Numerous real-world applications involve the filtering problem: one aims to sequentially estimate the states of a (stochastic) dynamical system from incomplete, indirect, and noisy observations over time to forecast and control the underlying system. Examples can be found in econometrics, meteorology, robotics, bioinformatics, and beyond. In addition to the filtering problem, it is often of interest to estimate some parameters that govern the evolution of the system. Both the filtering and the parameter estimation can be naturally formalized under the Bayesian framework. However, the Bayesian solution poses some significant challenges. For example, the most widely used particle filters can suffer from particle degeneracy and the more robust ensemble Kalman filters rely on the rather restrictive Gaussian assumptions. Exploiting the interplay between the low-rank tensor structure and Markov property of the filtering problem, we present a computationally efficient measure transport approach for tackling Bayesian filtering and parameter inference altogether. The associated measure transport can also be used for solving other Bayesian inference problems.