13 research outputs found
Mean field analysis for Continuous Time Bayesian Networks
In this paper we investigate the use of the mean field technique to analyze Continuous Time Bayesian Networks (CTBN). They model continuous time evolving variables with exponentially distributed transition rates depending on the parent variables in the graph. CTBN inference consists of computing the probability distribution of a subset of variables, conditioned by the observation of other variables' values (evidence). The computation of exact results is often unfeasible due to the complexity of the model. For such reason, the possibility to perform the CTBN inference through the equivalent Generalized Stochastic Petri
Net (GSPN) was investigated in the past. In this paper instead, we explore the use of mean field approximation and apply it to a well-known epidemic case study. The CTBN model is converted in both a GSPN and in a mean field based model. The example is then analyzed with both solutions, in order to evaluate the accuracy of the mean field approximation for the computation of the posterior probability of the CTBN given an evidence. A summary of the lessons learned during this preliminary attempt concludes the paper
Fast MCMC sampling for Markov jump processes and extensions
Markov jump processes (or continuous-time Markov chains) are a simple and
important class of continuous-time dynamical systems. In this paper, we tackle
the problem of simulating from the posterior distribution over paths in these
models, given partial and noisy observations. Our approach is an auxiliary
variable Gibbs sampler, and is based on the idea of uniformization. This sets
up a Markov chain over paths by alternately sampling a finite set of virtual
jump times given the current path and then sampling a new path given the set of
extant and virtual jump times using a standard hidden Markov model forward
filtering-backward sampling algorithm. Our method is exact and does not involve
approximations like time-discretization. We demonstrate how our sampler extends
naturally to MJP-based models like Markov-modulated Poisson processes and
continuous-time Bayesian networks and show significant computational benefits
over state-of-the-art MCMC samplers for these models.Comment: Accepted at the Journal of Machine Learning Research (JMLR