Generalized Queries and Bayesian Statistical Model Checking in Dynamic Bayesian Networks: Application to Personalized Medicine

We introduce the concept of generalized probabilistic queries in Dynamic Bayesian Networks (DBN) - computing P(φ 1 |φ 2 ), where φ i is a formula in temporal logic encoding an equivalence class of trajectories through the variables of the model. Generalized queries include as special cases traditional query types for DBNs (i.e., filtering, smoothing, prediction, and classification), but can also be used to express inference problems that are either impossible, or impractical to answer using traditional algorithms for inference in DBNs. We then discuss the relationship between answering generalized queries and the Probabilistic Model Checking Problem and introduce two novel algorithms for efficiently estimating (φ 1 |φ 2 ) in a Bayesian fashion. Finally, we demonstrate our method by answering generalized queries that arise in the context of critical care medicine. Specifically, we show that our approach can be used to make treatment decisions for a cohort of 1,000 simulated sepsis patients, and that it outperforms Support Vector Machines, Neural Networks, and Random Forests on the same task.