Graphical models allow a separation between qualitative, structural aspects of uncertain knowledge and the quantitative, parametric aspects of uncertainty—the former represented via patterns of edges in the graph and the latter represented as numerical values associated with subsets of nodes in the graph. This separation is often found to be natural by domain experts, taming some of the problems associated with structuring, interpreting, and troubleshooting the model. Even more importantly, the graph-theoretic framework has allowed for the development of general inference algorithms, which in many cases provide orders of magnitude speedups over brute-force methods.(see Decision trees_Old Kiwi).
