Refining a Bayesian network using a chain event graph

The search for a useful explanatory model based on a Bayesian Network (BN) now has a long and successful history. However, when the dependence structure between the variables of the problem is asymmetric then this cannot be captured by the BN. The Chain Event Graph (CEG) provides a richer class of models which incorporates these types of dependence structures as well as retaining the property that conclusions can be easily read back to the client. We demonstrate on a real health study how the CEG leads us to promising higher scoring models and further enables us to make more refined conclusions than can be made from the BN. Further we show how these graphs can express causal hypotheses about possible interventions that could be enforced

Structural-EM for Learning PDG Models from Incomplete Data

Probabilistic Decision Graphs (PDGs) are a class of graphical models that can naturally encode some context specific independencies that cannot always be efficiently captured by other popular models, such as Bayesian Networks. Furthermore, inference can be carried out efficiently over a PDG, in time linear in the size of the model. The problem of learning PDGs from data has been studied in the literature, but only for the case of complete data. In this paper we propose an algorithm for learning PDGs in the presence of missing data. The proposed method is based on the EM algorithm for estimating the structure of the model as well as the parameters. We test our proposal on artificially generated data with different rates of missing cells, showing a reasonable performance