Learning and predicting with chain event graphs

Abstract

Graphical models provide a very promising avenue for making sense of large, complex datasets. The most popular graphical models in use at the moment are Bayesian networks (BNs). This thesis shows, however, they are not always ideal factorisations of a system. Instead, I advocate for the use of a relatively new graphical model, the chain event graph (CEG), that is based on event trees. Event trees directly represent graphically the event space of a system. Chain event graphs reduce their potentially huge dimensionality by taking into account identical probability distributions on some of the event tree’s subtrees, with the added benefits of showing the conditional independence relationships of the system — one of the advantages of the Bayesian network representation that event trees lack — and implementation of causal hypotheses that is just as easy, and arguably more natural, than is the case with Bayesian networks, with a larger domain of implementation using purely graphical means. The trade-off for this greater expressive power, however, is that model specification and selection are much more difficult to undertake with the larger set of possible models for a given set of variables. My thesis is the first exposition of how to learn CEGs. I demonstrate that not only is conjugate (and hence quick) learning of CEGs possible, but I characterise priors that imply conjugate updating based on very reasonable assumptions that also have direct Bayesian network analogues. By re-casting CEGs as partition models, I show how established partition learning algorithms can be adapted for the task of learning CEGs. I then develop a robust yet flexible prediction machine based on CEGs for any discrete multivariate time series — the dynamic CEG model — which combines the power of CEGs, multi-process and steady modelling, lattice theory and Occam’s razor. This is also an exact method that produces reliable predictions without requiring much a priori modelling. I then demonstrate how easily causal analysis can be implemented with this model class that can express a wide variety of causal hypotheses. I end with an application of these techniques to real educational data, drawing inferences that would not have been possible simply using BNs