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

This paper introduces the factored conditional filter, a new filtering algorithm for simultaneously tracking states and estimating parameters in high-dimensional state spaces. The conditional nature of the algorithm 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 algorithm 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.