Open AccessProceedings Article
Thin Junction Trees
Francis Bach,Michael I. Jordan +1 more
- 03 Jan 2001
- Vol. 14, pp 569-576
TL;DR: An algorithm is presented that induces a class of models with thin junction trees—models that are characterized by an upper bound on the size of the maximal cliques of their triangulated graph that allows both an efficient implementation of an iterative scaling parameter estimation algorithm and also ensures that inference can be performed efficiently with the final model.
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Abstract: We present an algorithm that induces a class of models with thin junction trees—models that are characterized by an upper bound on the size of the maximal cliques of their triangulated graph. By ensuring that the junction tree is thin, inference in our models remains tractable throughout the learning process. This allows both an efficient implementation of an iterative scaling parameter estimation algorithm and also ensures that inference can be performed efficiently with the final model. We illustrate the approach with applications in handwritten digit recognition and DNA splice site detection.
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Approximating discrete probability distributions with dependence trees
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A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
TL;DR: Every minor-closed class of graphs that does not contain all planar graphs has a linear-time recognition algorithm that determines whether the treewidth of G is at most at most some constant $k$ and finds a tree-decomposition of G withtreewidth at most k.
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Probabilistic Networks and Expert Systems
Robert G. Cowell,Steffen L. Lauritzen,A. Philip David,David Spiegelhalter,V. Nair,J. Lawless,Michael I. Jordan +6 more
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TL;DR: This book gives a thorough and rigorous mathematical treatment of the underlying ideas, structures, and algorithms of probabilistic expert systems, emphasizing those cases in which exact answers are obtainable.
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$I$-Divergence Geometry of Probability Distributions and Minimization Problems
TL;DR: In this article, the minimum discrimination information problem is viewed as projecting a PD onto a convex set of PD's and useful existence theorems for and characterizations of the minimizing PD are arrived at.