Deterministic Anytime Inference for Stochastic Continuous-Time Markov Processes

We describe a deterministic anytime method for calculating filtered and smoothed distributions in large variable-based continuous time Markov processes. Prior non-random algorithms do not converge to the true distribution in the limit of infinite computation time. Sampling algorithms give different results each time run, which can lead to instability when used inside expectation-maximization or other algorithms. Our method combines the anytime convergent properties of sampling with the non-random nature of variational approaches. It is built upon a sum of time-ordered products, an expansion of the matrix exponential. We demonstrate that our method performs as well as or better than the current best sampling approaches on benchmark problems.