Graphical decompositions

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 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 ...

Approximate Inference in Graphical Models using Tensor Decompositions

We demonstrate that tensor decompositions can be used to transform graphical models into structurally simpler graphical models that approximate the same joint probability distribution. In this way, standard inference algorithms such as the junction tree algorithm, can be used in order to use the transformed graphical model for approximate inference. The usefulness of the technique is demonstrat...

Graphical Abstracts

Finding Branch-Decompositions and Rank-Decompositions

We present a new algorithm that can output the rank-decomposition of width at most k of a graph if such exists. For that we use an algorithm that, for an input matroid represented over a fixed finite field, outputs its branch-decomposition of width at most k if such exists. This algorithm works also for partitioned matroids. Both these algorithms are fixed-parameter tractable, that is, they run...