Unifying tree decompositions for reasoning in graphical models

Unifying Cluster-Tree Decompositions for Reasoning in Graphical models∗

The paper provides a unifying perspective of tree-decomposition algorithms appearing in various automated reasoning areas such as join-tree clustering for constraint-satisfaction and the clique-tree algorithm for probabilistic reasoning. Within this framework, we introduce a new algorithm, called bucket-tree elimination (BTE), that extends Bucket Elimination (BE) to trees, and show that it can ...

Unifying tree decompositions for reasoning in graphical models

The paper provides a unifying perspective of tree-decomposition algorithms appearing in various automated reasoning areas such as join-tree clustering for constraint-satisfaction and the cliquetree algorithm for probabilistic reasoning. Within this framework, we introduce a new algorithm, called bucket-tree elimination (BTE), that extends Bucket Elimination (BE) to trees, and show that it can p...

Unifying Cluster-Tree Decompositions for Automated Reasoning

The paper provides a unifying perspective of tree-decomposition algorithms appearing in various automated reasoning areas such as jointree clustering for constraint-satisfaction and the clique-tree algorithm for probabilistic reasoning. By following the framework introduced by Shenoy [16], we then introduce a new algorithm, called buckettree elimination (BTE), that extends Bucket Elimination (B...

Reasoning with Graphical Models

Blossom Tree Graphical Models

We combine the ideas behind trees and Gaussian graphical models to form a new nonparametric family of graphical models. Our approach is to attach nonparanormal “blossoms”, with arbitrary graphs, to a collection of nonparametric trees. The tree edges are chosen to connect variables that most violate joint Gaussianity. The non-tree edges are partitioned into disjoint groups, and assigned to tree ...