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Representational capabilities

If graphical representations are natural for human intuition, then the subclass of tree models are particularly intuitive. Trees are sparse graphs, having $n-1$ or fewer edges. There is at most one path between every pair of variables; thus, independence relationships between subsets of variables, which are not easy to read out in general Bayesian network topologies, are obvious in a tree. In a tree, an edge corresponds to the simple, common-sense notion of direct dependency and is the natural representation for it. However, the very simplicity that makes tree models appealing also limits their modeling power. Note that the number of free parameters in a tree grows linearly with $n$ while the size of the state space $\Omega(V)$ is an exponential function of $n$. Thus the class of dependency structures representable by trees is a relatively small one.

Journal of Machine Learning Research 2000-10-19