School of Computing Research Colloquia

Refining MAP model selection using trees

Peter Thwaites (School of Mathematics, University of Leeds)

Abstract: Recent developments in the representation of discrete statistical processes have resulted in a number of graphical models which represent problem asymmetry explicitly within the topology of the graph. The most useful of these graphs is the Chain Event Graph (Smith, Thwaites & others, 2006 on), but here I will concentrate on the related class of coloured trees. These can be used to express a richer set of conditional independence (Markov) statements than are expressible through a single Bayesian Network (BN). The class of BNs is contained within the class of coloured trees, and we can exploit this property, since it follows that BN model selection procedures can be nested within those for coloured trees. One can devise a score function for trees so that if a model can be represented as both a BN and a tree, then the tree-based score is equal to the BN-based one. If a problem incorporates significant context-specific conditional independence structure, we can use BN-based learning to select a good approximate model, and then tree-based learning methods to further refine this model.