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The junction tree algorithm (also known as 'Clique Tree') is a method used in machine learning to extract marginalization in general graphs. In essence, it entails performing belief propagation on a modified graph called a junction tree. The graph is called a tree because it branches into different sections of data; nodes of variables are the ...
Each tree node lists at most three vertices, so the width of this decomposition is two. In graph theory, a tree decomposition is a mapping of a graph into a tree that can be used to define the treewidth of the graph and speed up solving certain computational problems on the graph. Tree decompositions are also called junction trees, clique trees ...
In graph theory, a moral graph is used to find the equivalent undirected form of a directed acyclic graph. It is a key step of the junction tree algorithm , used in belief propagation on graphical models .
One method of exact marginalization in general graphs is called the junction tree algorithm, which is simply belief propagation on a modified graph guaranteed to be a tree. The basic premise is to eliminate cycles by clustering them into single nodes.
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 ...
Graph reduction; Graph-structured stack; Graphical model. Bayesian network; D-separation; Markov random field; Tree decomposition (Junction tree) and treewidth; Graph triangulation (see also Chordal graph) Perfect order; Hidden Markov model. Baum–Welch algorithm; Viterbi algorithm; Incidence matrix; Independent set problem; Knowledge ...
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A tree decomposition of an arbitrary constraint satisfaction problem is a tree decomposition of its primal graph. Every constraint can be enforced on a node of the tree because each constraint creates a clique on its variables on the primal graph and, for every tree decomposition, the variables of a clique are completely contained in the ...