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Then any maximum-weight spanning tree of the clique graph is a junction tree. So, to construct a junction tree we just have to extract a maximum weight spanning tree out of the clique graph. This can be efficiently done by, for example, modifying Kruskal's algorithm. The last step is to apply belief propagation to the obtained junction tree. [10]
The tree decomposition of a graph is far from unique; for example, a trivial tree decomposition contains all vertices of the graph in its single root node. A tree decomposition in which the underlying tree is a path graph is called a path decomposition, and the width parameter derived from these special types of tree decompositions is known as ...
For the given set of local domains as input, we find out if we can create a junction tree, either by using the set directly or by adding dummy domains to the set first and then creating the junction tree, if construction junction is not possible then algorithm output that there is no way to reduce the number of steps to compute the given ...
Felsenstein's tree-pruning algorithm – statistical genetics; ... Junction tree algorithm; K ... Stein's example. Proof of Stein's example;
A clique tree or junction tree is a tree of cliques, used in the junction tree algorithm. A chain graph is a graph which may have both directed and undirected edges, but without any directed cycles (i.e. if we start at any vertex and move along the graph respecting the directions of any arrows, we cannot return to the vertex we started from if ...
An alternative characterization of chordal graphs, due to Gavril (1974), involves trees and their subtrees. From a collection of subtrees of a tree, one can define a subtree graph, which is an intersection graph that has one vertex per subtree and an edge connecting any two subtrees that overlap in one or more nodes of the tree. Gavril showed ...
Chow and Liu provide a simple algorithm for constructing the optimal tree; at each stage of the procedure the algorithm simply adds the maximum mutual information pair to the tree. See the original paper, Chow & Liu (1968), for full details. A more efficient tree construction algorithm for the common case of sparse data was outlined in Meilă ...
It is a key step of the junction tree algorithm, used in belief propagation on graphical models. A directed acyclic graph The corresponding moral graph, with newly added arcs shown in red