A Study of Chain Graph Interpretations

Probabilistic graphical models are today one of the most well used architec-tures for modelling and reasoning about knowledge with uncertainty. Themost widely used subclass of these models is Bayesian networks that hasfound a wide range of applications both in industry and research. Bayesiannetworks do however have a major limitation which is that only asymmetricrelationships, namely cause and effect relationships, can be modelled be-tween its variables. A class of probabilistic graphical models that has triedto solve this shortcoming is chain graphs. It is achieved by including twotypes of edges in the models, representing both symmetric and asymmetricrelationships between the connected variables. This allows for a wider rangeof independence models to be modelled. Depending on how the second edgeis interpreted this has also given rise to different chain graph interpretations.Although chain graphs were first presented in the late eighties the fieldhas been relatively dormant and most research has been focused on Bayesiannetworks. This was until recently when chain graphs got renewed interest.The research on chain graphs has thereafter extended many of the ideasfrom Bayesian networks and in this thesis we study what this new surge ofresearch has been focused on and what results have been achieved. Moreoverwe do also discuss what areas that we think are most important to focus onin further research. This work is funded by the Swedish Research Council (ref. 2010-4808).