Factored Conditional Filtering: Tracking States and Estimating Parameters in High-Dimensional Spaces

TL;DR

This paper presents factored conditional filters that decompose high-dimensional state spaces into low-dimensional subspaces, enabling efficient simultaneous tracking of states and estimation of parameters, with demonstrated success in epidemic and network applications.

Contribution

Introduction of factored conditional filtering algorithms that decompose high-dimensional problems into manageable subspaces for improved tracking and parameter estimation.

Findings

Effective in tracking epidemics.

Accurate parameter estimation in large networks.

Applicable under common conditions in engineering and geophysics.

Abstract

This paper introduces factored conditional filters, new filtering algorithms for simultaneously tracking states and estimating parameters in high-dimensional state spaces. The conditional nature of the algorithms is used to estimate parameters and the factored nature is used to decompose the state space into low-dimensional subspaces in such a way that filtering on these subspaces gives distributions whose product is a good approximation to the distribution on the entire state space. The conditions for successful application of the algorithms are that observations be available at the subspace level and that the transition model can be factored into local transition models that are approximately confined to the subspaces; these conditions are widely satisfied in computer science, engineering, and geophysical filtering applications. We give experimental results on tracking epidemics and estimating parameters in large contact networks that show the effectiveness of our approach.