An extended depth-first search algorithm for optimal triangulation of Bayesian networks

Li, Chao; Ueno, Maomi

doi:10.1016/j.ijar.2016.09.012

Cited by 14 publications

(11 citation statements)

References 14 publications

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“…Many different chordal graphs with different tree width may be generated from a given graph with loops, a number of algorithms are available to perform triangulation and construct chordal graphs. [7][8][9][10] However, no algorithm is able to ensure finding the best triangulation scheme corresponding to the ( or one of if multiple chordal graphs with the same tree width exist) smallest tree width.…”

Section: Junction Tree Algorithm Loopy and Gaussian Belief Propagationmentioning

confidence: 99%

Factorization in Molecular Modeling and Belief Propagation Algorithms

Tian¹

2021

Preprint

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Factorization reduces computational complexity and is therefore an important tool in statistical machine learning of high dimensional systems. Conventional molecular modeling, including molecular dynamics and Monte Carlo simulations of molecular systems, is a large research field based on approximate factorization of molecular interactions. Recently, the local distribution theory was proposed to factorize global joint distribution of a given molecular system into trainable local distributions. Belief propagation algorithms are a family of exact factorization algorithms for trees and are extended to approximate loopy belief propagation algorithms for graphs with loops. Despite the fact that factorization of probability distribution is their common foundation, computational research in molecular systems and machine learning studies utilizing belief propagation algorithms have been carried out independently with respective track of algorithm development. The connection and differences among these factorization algorithms are briefly presented in this perspective, with the hope to intrigue further development in factorization algorithms for physical modeling of complex molecular systems.

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Section: Junction Tree Algorithm Loopy and Gaussian Belief Propagationmentioning

confidence: 99%

Factorization in Molecular Modeling and Belief Propagation Algorithms

Tian¹

2021

Preprint

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“…DFS incorporated Genetic algorithm to discover the optimal processing sequence of features of a part (PSFP) that reduces the feature transitions' energy consumption by 28.60 % [11]. A smaller search space was explored faster with reduced cost by another extended depth-first search (EDFS) algorithm [32].…”

Section: Figure 1 Classification Of Path Planning Approachesmentioning

confidence: 99%

A review on graph search algorithms for optimal energy efficient path planning for an unmanned air vehicle

Debnath

Omar

Latip

et al. 2019

IJEECS

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<span>Unmanned Air Vehicle (UAV) has attracted attention in recent years in conducting missions for longer time with higher levels of autonomy. For the enhanced autonomous characteristic of UAV, path planning is one of the crucial issues. Current researches on the graph search algorithms under combinatorial method are mainly reviewed in this paper by keeping focus on the comprehensive surveys of its properties for path planning. The outcome is a pen picture of their assumptions and drawbacks.</span>

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“…If these two algorithms are not fast enough then it will be necessary to use more sophisticated algorithms such as the one by Yang et al, 35 and if a triangulation with minimal total size is required then it will be necessary to use an algorithm that achieves that purpose. 28,[31][32][33][34] There are other algorithms for thinning and algorithms that find a minimal triangulation in a single step, without thinning.…”

Section: Speed and Comparison With Other Algorithmsmentioning

confidence: 99%

Thinning a Triangulation of a Bayesian Network or Undirected Graph to Create a Minimal Triangulation

Jones

Didelez

2017

Int. J. Unc. Fuzz. Knowl. Based Syst.

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In one procedure for finding the maximal prime decomposition of a Bayesian network or undirected graphical model, the first step is to create a minimal triangulation of the network, and a common and straightforward way to do this is to create a triangulation that is not necessarily minimal and then thin this triangulation by removing excess edges. We show that the algorithm for thinning proposed in several previous publications is incorrect. A different version of this algorithm is available in the R package gRbase, but its correctness has not previously been proved. We prove that this version is correct and provide a simpler version, also with a proof. We compare the speed of the two corrected algorithms in three ways and find that asymptotically their speeds are the same, neither algorithm is consistently faster than the other, and in a computer experiment the algorithm used by gRbase is faster when the original graph is large, dense, and undirected, but usually slightly slower when it is directed.

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An extended depth-first search algorithm for optimal triangulation of Bayesian networks

Cited by 14 publications

References 14 publications

Factorization in Molecular Modeling and Belief Propagation Algorithms

Factorization in Molecular Modeling and Belief Propagation Algorithms

A review on graph search algorithms for optimal energy efficient path planning for an unmanned air vehicle

Thinning a Triangulation of a Bayesian Network or Undirected Graph to Create a Minimal Triangulation

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