Factored Filtering of Continuous-Time Systems
This addresses the computational bottleneck in filtering for large-scale continuous-time systems, but it is incremental as it builds on existing uniformization and approximation techniques.
The paper tackles the problem of filtering in continuous-time stochastic systems where the full state distribution is intractable, by approximating the belief as a product of marginals and using matrix exponential computations. The result shows that their factored uniformization method outperforms previous uniformization methods and mean field algorithms, with a demonstrated bound on KL-divergence.
We consider filtering for a continuous-time, or asynchronous, stochastic system where the full distribution over states is too large to be stored or calculated. We assume that the rate matrix of the system can be compactly represented and that the belief distribution is to be approximated as a product of marginals. The essential computation is the matrix exponential. We look at two different methods for its computation: ODE integration and uniformization of the Taylor expansion. For both we consider approximations in which only a factored belief state is maintained. For factored uniformization we demonstrate that the KL-divergence of the filtering is bounded. Our experimental results confirm our factored uniformization performs better than previously suggested uniformization methods and the mean field algorithm.