Belief Acquisition as Stochastic Filtering

Abstract

This paper studies how belief acquisition can be accomplished using stochastic filtering. First, a theoretical foundation for empirical beliefs is outlined. Then stochastic filtering in this context is studied. The 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 schema can be factored into local transition schemas that are approximately confined to the subspaces; these conditions are widely satisfied in computer science, engineering, and geophysical filtering applications. Experimental results on tracking epidemics and estimating parameters in large contact networks show the effectiveness of the approach.