The Robotics Institute

Carnegie Mellon Robotics Institute

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Abstract

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 parametrized product of Dirichlet distributions. Besides 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.

Keywords

graphical models, spanning tree, Bayesian learning

Notes

Sponsor: Office of Naval Research

Grant ID: N00014-98-C-0326

Associated Center(s) / Consortia: Vision and Autonomous Systems Center

Text Reference

Marina Meila and Tommi Jaakkola, "Tractable Bayesian Learning of Tree Belief Networks," tech. report CMU-RI-TR-00-15, Robotics Institute, Carnegie Mellon University, May, 2000

BibTeX Reference

@techreport{Meila_2000_3362,
   author = "Marina Meila and Tommi Jaakkola",
   title = "Tractable Bayesian Learning of Tree Belief Networks",
   booktitle = "",
   institution = "Robotics Institute",
   month = "May",
   year = "2000",
   number= "CMU-RI-TR-00-15",
   address= "Pittsburgh, PA",
}

The Robotics Institute

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