Tractable Bayesian Learning of Tree Belief Networks
This provides a tractable solution for Bayesian learning in tree-structured models, which is incremental as it builds on prior work like Heckerman et al. (1995).
The paper tackles the problem of Bayesian learning for tree belief networks by introducing decomposable priors that make exact posterior inference tractable in polynomial time, enabling exact Bayesian learning and a new class of latent variable models.
In this paper we present decomposable priors, a family of priors over structure and parameters of tree belief nets for which Bayesian learning with complete observations is tractable, in the sense that the posterior is also decomposable and can be completely determined analytically in polynomial time. This follows from two main results: First, we show that factored distributions over spanning trees in a graph can be integrated in closed form. Second, we examine priors over tree parameters and show that a set of assumptions similar to (Heckerman and al. 1995) constrain the tree parameter priors to be a compactly parameterized product of Dirichlet distributions. Beside allowing for exact Bayesian learning, these results permit us to formulate a new class of tractable latent variable models in which the likelihood of a data point is computed through an ensemble average over tree structures.