An Algorithm Based on Loop-Cutting Contribution Function for Loop Cutset Problem in Bayesian Network
The loop cutset solving algorithm in the Bayesian network is particularly important for Bayesian inference. This paper proposes an algorithm for solving the approximate minimum loop cutset based on the loop-cutting contribution index. Compared with the existing algorithms, the algorithm uses the loo...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/5/462 |
| _version_ | 1797395370976739328 |
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| author | Jie Wei Wenxian Xie Yufeng Nie |
| author_facet | Jie Wei Wenxian Xie Yufeng Nie |
| author_sort | Jie Wei |
| collection | DOAJ |
| description | The loop cutset solving algorithm in the Bayesian network is particularly important for Bayesian inference. This paper proposes an algorithm for solving the approximate minimum loop cutset based on the loop-cutting contribution index. Compared with the existing algorithms, the algorithm uses the loop-cutting contribution index of nodes and node-pairs to analyze nodes from a global perspective, and select loop cutset candidates with node-pair as the unit. The algorithm uses the parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula> to control the range of node-pairs, and the parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula> to control the selection conditions of the node-pairs, so that the algorithm can adjust the parameters according to the size of the Bayesian networks, which ensures computational efficiency. The numerical experiments show that the calculation efficiency of the algorithm is significantly improved when it is consistent with the accuracy of the existing algorithm; the experiments also studied the influence of parameter settings on calculation efficiency using trend analysis and two-way analysis of variance. The loop cutset solving algorithm based on the loop-cutting contribution index uses the node-pair as the unit to solve the loop cutset, which helps to improve the efficiency of Bayesian inference and Bayesian network structure analysis. |
| first_indexed | 2024-03-09T00:34:34Z |
| format | Article |
| id | doaj.art-6fdadf5babc14314ba40d371231d3643 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T00:34:34Z |
| publishDate | 2021-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-6fdadf5babc14314ba40d371231d36432023-12-11T18:16:45ZengMDPI AGMathematics2227-73902021-02-019546210.3390/math9050462An Algorithm Based on Loop-Cutting Contribution Function for Loop Cutset Problem in Bayesian NetworkJie Wei0Wenxian Xie1Yufeng Nie2School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, ChinaSchool of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, ChinaSchool of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, ChinaThe loop cutset solving algorithm in the Bayesian network is particularly important for Bayesian inference. This paper proposes an algorithm for solving the approximate minimum loop cutset based on the loop-cutting contribution index. Compared with the existing algorithms, the algorithm uses the loop-cutting contribution index of nodes and node-pairs to analyze nodes from a global perspective, and select loop cutset candidates with node-pair as the unit. The algorithm uses the parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula> to control the range of node-pairs, and the parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula> to control the selection conditions of the node-pairs, so that the algorithm can adjust the parameters according to the size of the Bayesian networks, which ensures computational efficiency. The numerical experiments show that the calculation efficiency of the algorithm is significantly improved when it is consistent with the accuracy of the existing algorithm; the experiments also studied the influence of parameter settings on calculation efficiency using trend analysis and two-way analysis of variance. The loop cutset solving algorithm based on the loop-cutting contribution index uses the node-pair as the unit to solve the loop cutset, which helps to improve the efficiency of Bayesian inference and Bayesian network structure analysis.https://www.mdpi.com/2227-7390/9/5/462bayesian networkloop cutsetloop cutset solving algorithmloop-cutting contributionnode-pair |
| spellingShingle | Jie Wei Wenxian Xie Yufeng Nie An Algorithm Based on Loop-Cutting Contribution Function for Loop Cutset Problem in Bayesian Network Mathematics bayesian network loop cutset loop cutset solving algorithm loop-cutting contribution node-pair |
| title | An Algorithm Based on Loop-Cutting Contribution Function for Loop Cutset Problem in Bayesian Network |
| title_full | An Algorithm Based on Loop-Cutting Contribution Function for Loop Cutset Problem in Bayesian Network |
| title_fullStr | An Algorithm Based on Loop-Cutting Contribution Function for Loop Cutset Problem in Bayesian Network |
| title_full_unstemmed | An Algorithm Based on Loop-Cutting Contribution Function for Loop Cutset Problem in Bayesian Network |
| title_short | An Algorithm Based on Loop-Cutting Contribution Function for Loop Cutset Problem in Bayesian Network |
| title_sort | algorithm based on loop cutting contribution function for loop cutset problem in bayesian network |
| topic | bayesian network loop cutset loop cutset solving algorithm loop-cutting contribution node-pair |
| url | https://www.mdpi.com/2227-7390/9/5/462 |
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