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In this paper we present decomposable priors, a family of priors overstructure and parameters of tree belief nets for which Bayesian learning withcomplete observations is tractable, in the sense that the posterior is alsodecomposable and can be completely determined analytically in polynomial time.This follows from two main results: First, we show that factored distributionsover spanning trees in a graph can be integrated in closed form. Second, weexamine priors over tree parameters and show that a set of assumptions similarto (Heckerman and al. 1995) constrain the tree parameter priors to be acompactly parameterized product of Dirichlet distributions. Beside allowing forexact Bayesian learning, these results permit us to formulate a new class oftractable latent variable models in which the likelihood of a data point iscomputed through an ensemble average over tree structures.

Tractable Bayesian Learning of Tree Belief Networks