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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 .
Tree decompositions are also called junction trees, clique trees, or join trees. ... The time dependence of this algorithm on k is an exponential function of k 3.
The algorithm was first proposed by Judea Pearl in 1982, [2] who formulated it as an exact inference algorithm on trees, later extended to polytrees. [3] While the algorithm is not exact on general graphs, it has been shown to be a useful approximate algorithm.
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 ...
Join follows the right spine of t 1 until a node c which is balanced with t 2. At this point a new node with left child c, root k and right child t 2 is created to replace c. The new node may invalidate the balancing invariant. This can be fixed with rotations. The following is the join algorithms on different balancing schemes. The join ...
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 ...
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 ...
As a result, the original problem can be solved by first translating it and then solving the resulting problem; however, this algorithm is polynomial-time only if the decomposition does not increase size superpolynomially. The width of a decomposition method is a measure of the size of problem it produced. Originally, the width was defined as ...