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This problem can be efficiently solved by calculating a maximum weight spanning tree from a fully connected indirected graph, where vertices are the developmental stages (1,…, L) and the weight of an edge (u, v) is equal to the mutual information between the corresponding variables (X u, X v ) (Chow and Liu, 1968).
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To tackle this issue, we compute the so-called maximum weight spanning tree (MWST).
By developing a maximum weighted spanning tree, TAN achieves a globally optimal trade-off between the complexity and learnability of the model.
The goal is to find a minimum weight spanning tree that uses at most K distinct labels.
We present constant factor approximation algorithms for the following two problems: First, given a connected graph G="(V,E) with non-negative edge weights, find a minimum weight spanning tree that respects prescribed upper bounds on the vertex degrees.
The learning method has been able to process five thousands genes and the network simplification through the maximum weighted spanning tree provided a graphical display of the huge network.
We then build the minimum weight spanning tree between connected components.
From a purely graph-theoretic point of view, the problem is simply finding a minimum-weight spanning tree through a graph with weighted edges, where domain-specific information is used to compute the weights.
The minimum-weight spanning tree problem is one of the most typical and well-known problems of combinatorial optimisation.
It is easy to see that the weight of a maximum spanning tree is no less than 1/ k − 1) of the summed edge weight of 𝒢, given the simple observation that each edge in 𝒢 is either an edge of the maximum spanning tree or adjacent to an edge of the maximum spanning tree with an equal or heavier weight (Claim 3).
In MTreeMix, the estimation of a single tree is based on solving a maximum weight branching problem by a combinatorial algorithm.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com