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.