Junction tree algorithm - Revision history

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	\| doi = 10.1109/cerma.2009.28		\| doi = 10.1109/cerma.2009.28
	\| publisher = IEEE		\| publisher = IEEE
	\| title = 2009 Electronics, Robotics and Automotive Mechanics Conference (CERMA)}}</ref> A specific use could be found in [[Autoencoder\|auto encoders]], which combine the graph and a passing network on a large scale automatically.<ref>{{Cite journal\|last=Jin\|first=Wengong\|date=Feb 2018\|title=Junction Tree Variational Autoencoder for Molecular Graph Generation\|journal=Cornell University\|arxiv=1802.04364\|bibcode=2018arXiv180204364J}}</ref>		\| title = 2009 Electronics, Robotics and Automotive Mechanics Conference (CERMA)\| pages = 301–306
			\| isbn = 978-0-7695-3799-3
			}}</ref> A specific use could be found in [[Autoencoder\|auto encoders]], which combine the graph and a passing network on a large scale automatically.<ref>{{Cite journal\|last=Jin\|first=Wengong\|date=Feb 2018\|title=Junction Tree Variational Autoencoder for Molecular Graph Generation\|journal=Cornell University\|arxiv=1802.04364\|bibcode=2018arXiv180204364J}}</ref>

	=== Inference Algorithms ===		=== Inference Algorithms ===

JJMC89 bot III: Moving :Category:Algorithms in graph theory to :Category:Graph algorithms per Wikipedia:Categories for discussion/Log/2024 October 4

2024-10-12T19:56:41Z

Moving Category:Algorithms in graph theory to Category:Graph algorithms per Wikipedia:Categories for discussion/Log/2024 October 4

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	{{DEFAULTSORT:Junction Tree Algorithm}}		{{DEFAULTSORT:Junction Tree Algorithm}}
	[[Category:Bayesian networks]]		[[Category:Bayesian networks]]
	[[Category:~~Algorithms~~ ~~in graph theory~~]]		[[Category:Graph algorithms]]

JJMC89 bot III: Moving :Category:Graph algorithms to :Category:Algorithms in graph theory per Wikipedia:Categories for discussion/Log/2024 October 4#Category:Graph algorithms

2024-10-12T02:23:54Z

Moving Category:Graph algorithms to Category:Algorithms in graph theory per Wikipedia:Categories for discussion/Log/2024 October 4#Category:Graph algorithms

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	{{DEFAULTSORT:Junction Tree Algorithm}}		{{DEFAULTSORT:Junction Tree Algorithm}}
	[[Category:Bayesian networks]]		[[Category:Bayesian networks]]
	[[Category:~~Graph~~ ~~algorithms~~]]		[[Category:Algorithms in graph theory]]

David Eppstein: /* Underlying theory */ cite conference not cite journal

2024-04-08T07:02:39Z

Underlying theory: cite conference not cite journal

← Previous revision		Revision as of 07:02, 8 April 2024
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	The last step is to apply [[belief propagation]] to the obtained junction tree.<ref>{{cite web \|url=https://www.cs.helsinki.fi/u/bmmalone/probabilistic-models-spring-2014/JunctionTreeBarber.pdf \|title= Probabilistic Modelling and Reasoning, The Junction Tree Algorithm \|last= Barber\|first=David \|date= 28 January 2014\|website= University of Helsinki \|access-date=16 November 2016}}</ref>		The last step is to apply [[belief propagation]] to the obtained junction tree.<ref>{{cite web \|url=https://www.cs.helsinki.fi/u/bmmalone/probabilistic-models-spring-2014/JunctionTreeBarber.pdf \|title= Probabilistic Modelling and Reasoning, The Junction Tree Algorithm \|last= Barber\|first=David \|date= 28 January 2014\|website= University of Helsinki \|access-date=16 November 2016}}</ref>

	'''Usage:''' A junction tree graph is used to visualize the probabilities of the problem. The tree can become a binary tree to form the actual building of the tree.<ref>{{~~Cite~~ ~~journal~~\|~~title~~=Fault Diagnosis in an Industrial Process Using Bayesian Networks: Application of the Junction Tree Algorithm - ~~IEEE~~ ~~Conference~~ ~~Publication\|language=en-US~~\|doi=10.1109/~~CERMA~~.2009.28\|~~s2cid~~=~~6068245~~}}</ref> A specific use could be found in [[Autoencoder\|auto encoders]], which combine the graph and a passing network on a large scale automatically.<ref>{{Cite journal\|last=Jin\|first=Wengong\|date=Feb 2018\|title=Junction Tree Variational Autoencoder for Molecular Graph Generation\|journal=Cornell University\|arxiv=1802.04364\|bibcode=2018arXiv180204364J}}</ref>		'''Usage:''' A junction tree graph is used to visualize the probabilities of the problem. The tree can become a binary tree to form the actual building of the tree.<ref>{{cite conference
			\| last1 = Ramirez \| first1 = Julio C.
			\| last2 = Munoz \| first2 = Guillermina
			\| last3 = Gutierrez \| first3 = Ludivina
			\| contribution = Fault Diagnosis in an Industrial Process Using Bayesian Networks: Application of the Junction Tree Algorithm
			\| date = September 2009
			\| doi = 10.1109/cerma.2009.28
			\| publisher = IEEE
			\| title = 2009 Electronics, Robotics and Automotive Mechanics Conference (CERMA)}}</ref> A specific use could be found in [[Autoencoder\|auto encoders]], which combine the graph and a passing network on a large scale automatically.<ref>{{Cite journal\|last=Jin\|first=Wengong\|date=Feb 2018\|title=Junction Tree Variational Autoencoder for Molecular Graph Generation\|journal=Cornell University\|arxiv=1802.04364\|bibcode=2018arXiv180204364J}}</ref>

	=== Inference Algorithms ===		=== Inference Algorithms ===

David Eppstein: /* References */ split off further reading and rm dup

2024-04-08T07:01:26Z

References: split off further reading and rm dup

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	==References==		==References==
	{{reflist}}		{{reflist}}

			==Further reading==
	* {{cite journal		* {{cite journal
	\| last = Lauritzen		\| last = Lauritzen
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	\| doi = 10.1016/S0888-613X(96)00069-2\| citeseerx = 10.1.1.47.3279		\| doi = 10.1016/S0888-613X(96)00069-2\| citeseerx = 10.1.1.47.3279
	}}		}}
	* {{cite journal\|last=Paskin \|first=Mark A. \|title=A Short Course on Graphical Models : 3. The Junction Tree Algorithms \|url=https://ai.stanford.edu/~paskin/gm-short-course/lec3.pdf \|url-status=unfit \|archive-url=https://web.archive.org/web/20150319085443/https://ai.stanford.edu/~paskin/gm-short-course/lec3.pdf \|archive-date=March 19, 2015 }}
	*Lepar, V., Shenoy, P. (1998). "A Comparison of Lauritzen-Spiegelhalter, Hugin, and Shenoy-Shafer Architectures for Computing Marginals of Probability Distributions." https://arxiv.org/ftp/arxiv/papers/1301/1301.7394.pdf		*Lepar, V., Shenoy, P. (1998). "A Comparison of Lauritzen-Spiegelhalter, Hugin, and Shenoy-Shafer Architectures for Computing Marginals of Probability Distributions." https://arxiv.org/ftp/arxiv/papers/1301/1301.7394.pdf

Cadduk: Wrong wikilink

2023-11-10T07:56:14Z

Wrong wikilink

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	* Multiple recursions of the Shafer-Shenoy algorithm results in Hugin algorithm<ref name=":3">{{Cite web\|url=https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-438-algorithms-for-inference-fall-2014/lecture-notes/MIT6_438F14_Lec14.pdf\|title=Algorithms\|date=2014\|website=Massachusetts Institute of Technology}}</ref>		* Multiple recursions of the Shafer-Shenoy algorithm results in Hugin algorithm<ref name=":3">{{Cite web\|url=https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-438-algorithms-for-inference-fall-2014/lecture-notes/MIT6_438F14_Lec14.pdf\|title=Algorithms\|date=2014\|website=Massachusetts Institute of Technology}}</ref>
	* Found by the [[Message passing in computer clusters\|message passing]] equation<ref name=":3" />		* Found by the [[Message passing in computer clusters\|message passing]] equation<ref name=":3" />
	*[[~~Separatrix~~ ~~(mathematics)~~\|Separator]] potentials are not stored<ref>{{Cite web\|url=https://cs.nyu.edu/~roweis/csc412-2004/notes/lec20x.pdf\|title=Hugin Inference Algorithm\|last=Roweis\|first=Sam\|date=2004\|website=NYU}}</ref>		*[[Vertex separator\|Separator]] potentials are not stored<ref>{{Cite web\|url=https://cs.nyu.edu/~roweis/csc412-2004/notes/lec20x.pdf\|title=Hugin Inference Algorithm\|last=Roweis\|first=Sam\|date=2004\|website=NYU}}</ref>

	The Shafer-Shenoy [[algorithm]] is the [[Sum-product algorithm\|sum product]] of a junction tree.<ref>{{Cite web\|url=https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-438-algorithms-for-inference-fall-2014/recitations/MIT6_438F14_rec8.pdf\|title=Algorithms for Inference\|date=2014\|website=Massachusetts Institute of Technology}}</ref> It is used because it runs programs and queries more efficiently than the Hugin algorithm. The algorithm makes calculations for conditionals for [[belief functions]] possible.<ref name=":02">{{cite arXiv\|last=Kłopotek\|first=Mieczysław A.\|date=2018-06-06\|title=Dempsterian-Shaferian Belief Network From Data\|eprint=1806.02373\|class=cs.AI}}</ref> [[Joint distributions]] are needed to make local computations happen.<ref name=":02" />		The Shafer-Shenoy [[algorithm]] is the [[Sum-product algorithm\|sum product]] of a junction tree.<ref>{{Cite web\|url=https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-438-algorithms-for-inference-fall-2014/recitations/MIT6_438F14_rec8.pdf\|title=Algorithms for Inference\|date=2014\|website=Massachusetts Institute of Technology}}</ref> It is used because it runs programs and queries more efficiently than the Hugin algorithm. The algorithm makes calculations for conditionals for [[belief functions]] possible.<ref name=":02">{{cite arXiv\|last=Kłopotek\|first=Mieczysław A.\|date=2018-06-06\|title=Dempsterian-Shaferian Belief Network From Data\|eprint=1806.02373\|class=cs.AI}}</ref> [[Joint distributions]] are needed to make local computations happen.<ref name=":02" />

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2022-01-30T15:31:59Z

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← Previous revision		Revision as of 15:31, 30 January 2022
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	*[[Separatrix (mathematics)\|Separator]] potentials are not stored<ref>{{Cite web\|url=https://cs.nyu.edu/~roweis/csc412-2004/notes/lec20x.pdf\|title=Hugin Inference Algorithm\|last=Roweis\|first=Sam\|date=2004\|website=NYU}}</ref>		*[[Separatrix (mathematics)\|Separator]] potentials are not stored<ref>{{Cite web\|url=https://cs.nyu.edu/~roweis/csc412-2004/notes/lec20x.pdf\|title=Hugin Inference Algorithm\|last=Roweis\|first=Sam\|date=2004\|website=NYU}}</ref>

	The Shafer-Shenoy [[algorithm]] is the [[Sum-product algorithm\|sum product]] of a junction tree.<ref>{{Cite web\|url=https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-438-algorithms-for-inference-fall-2014/recitations/MIT6_438F14_rec8.pdf\|title=Algorithms for Inference\|date=2014\|website=Massachusetts Institute of Technology}}</ref> It is used because it runs programs and queries more efficiently than the Hugin algorithm. The algorithm makes calculations for conditionals for [[belief functions]] possible.<ref name=":02">{{cite ~~arxiv~~\|last=Kłopotek\|first=Mieczysław A.\|date=2018-06-06\|title=Dempsterian-Shaferian Belief Network From Data\|eprint=1806.02373\|class=cs.AI}}</ref> [[Joint distributions]] are needed to make local computations happen.<ref name=":02" />		The Shafer-Shenoy [[algorithm]] is the [[Sum-product algorithm\|sum product]] of a junction tree.<ref>{{Cite web\|url=https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-438-algorithms-for-inference-fall-2014/recitations/MIT6_438F14_rec8.pdf\|title=Algorithms for Inference\|date=2014\|website=Massachusetts Institute of Technology}}</ref> It is used because it runs programs and queries more efficiently than the Hugin algorithm. The algorithm makes calculations for conditionals for [[belief functions]] possible.<ref name=":02">{{cite arXiv\|last=Kłopotek\|first=Mieczysław A.\|date=2018-06-06\|title=Dempsterian-Shaferian Belief Network From Data\|eprint=1806.02373\|class=cs.AI}}</ref> [[Joint distributions]] are needed to make local computations happen.<ref name=":02" />

	===Underlying theory===		===Underlying theory===

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2022-01-21T10:06:57Z

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← Previous revision		Revision as of 10:06, 21 January 2022
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	The last step is to apply [[belief propagation]] to the obtained junction tree.<ref>{{cite web \|url=https://www.cs.helsinki.fi/u/bmmalone/probabilistic-models-spring-2014/JunctionTreeBarber.pdf \|title= Probabilistic Modelling and Reasoning, The Junction Tree Algorithm \|last= Barber\|first=David \|date= 28 January 2014\|website= University of Helsinki \|access-date=16 November 2016}}</ref>		The last step is to apply [[belief propagation]] to the obtained junction tree.<ref>{{cite web \|url=https://www.cs.helsinki.fi/u/bmmalone/probabilistic-models-spring-2014/JunctionTreeBarber.pdf \|title= Probabilistic Modelling and Reasoning, The Junction Tree Algorithm \|last= Barber\|first=David \|date= 28 January 2014\|website= University of Helsinki \|access-date=16 November 2016}}</ref>

	'''Usage:''' A junction tree graph is used to visualize the probabilities of the problem. The tree can become a binary tree to form the actual building of the tree.<ref>{{Cite ~~document~~\|title=Fault Diagnosis in an Industrial Process Using Bayesian Networks: Application of the Junction Tree Algorithm - IEEE Conference Publication\|language=en-US\|doi=10.1109/CERMA.2009.28\|s2cid=6068245}}</ref> A specific use could be found in [[Autoencoder\|auto encoders]], which combine the graph and a passing network on a large scale automatically.<ref>{{Cite journal\|last=Jin\|first=Wengong\|date=Feb 2018\|title=Junction Tree Variational Autoencoder for Molecular Graph Generation\|journal=Cornell University\|arxiv=1802.04364\|bibcode=2018arXiv180204364J}}</ref>		'''Usage:''' A junction tree graph is used to visualize the probabilities of the problem. The tree can become a binary tree to form the actual building of the tree.<ref>{{Cite journal\|title=Fault Diagnosis in an Industrial Process Using Bayesian Networks: Application of the Junction Tree Algorithm - IEEE Conference Publication\|language=en-US\|doi=10.1109/CERMA.2009.28\|s2cid=6068245}}</ref> A specific use could be found in [[Autoencoder\|auto encoders]], which combine the graph and a passing network on a large scale automatically.<ref>{{Cite journal\|last=Jin\|first=Wengong\|date=Feb 2018\|title=Junction Tree Variational Autoencoder for Molecular Graph Generation\|journal=Cornell University\|arxiv=1802.04364\|bibcode=2018arXiv180204364J}}</ref>

	=== Inference Algorithms ===		=== Inference Algorithms ===

GoodDay at 02:48, 27 August 2021

2021-08-27T02:48:45Z

← Previous revision		Revision as of 02:48, 27 August 2021
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	[[File:Junction-tree-example.gif\|thumb\|Example of a junction tree]]		[[File:Junction-tree-example.gif\|300px\|thumb\|Example of a junction tree]]
	The '''junction tree algorithm''' (also known as 'Clique Tree') is a method used in [[machine learning]] to extract [[marginal distribution\|marginalization]] in general [[Graph (discrete mathematics)\|graph]]s. 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; [[Vertex (graph theory)\|nodes]] of variables are the branches.<ref name=":1">{{Cite web\|url=https://ai.stanford.edu/~paskin/gm-short-course/lec3.pdf\|title=A Short Course on Graphical Models\|last=Paskin\|first=Mark\|website=Stanford}}</ref> The basic premise is to eliminate [[cycle (graph theory)\|cycle]]s by clustering them into single nodes. Multiple extensive classes of queries can be compiled at the same time into larger structures of data.<ref name=":1" /> There are different [[algorithm]]s to meet specific needs and for what needs to be calculated. [[Inference network\|Inference algorithms]] gather new developments in the data and calculate it based on the new information provided.<ref>{{Cite web\|url=http://www.dfki.de/~neumann/publications/diss/node58.html\|title=The Inference Algorithm\|website=www.dfki.de\|access-date=2018-10-25}}</ref>		The '''junction tree algorithm''' (also known as 'Clique Tree') is a method used in [[machine learning]] to extract [[marginal distribution\|marginalization]] in general [[Graph (discrete mathematics)\|graph]]s. 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; [[Vertex (graph theory)\|nodes]] of variables are the branches.<ref name=":1">{{Cite web\|url=https://ai.stanford.edu/~paskin/gm-short-course/lec3.pdf\|title=A Short Course on Graphical Models\|last=Paskin\|first=Mark\|website=Stanford}}</ref> The basic premise is to eliminate [[cycle (graph theory)\|cycle]]s by clustering them into single nodes. Multiple extensive classes of queries can be compiled at the same time into larger structures of data.<ref name=":1" /> There are different [[algorithm]]s to meet specific needs and for what needs to be calculated. [[Inference network\|Inference algorithms]] gather new developments in the data and calculate it based on the new information provided.<ref>{{Cite web\|url=http://www.dfki.de/~neumann/publications/diss/node58.html\|title=The Inference Algorithm\|website=www.dfki.de\|access-date=2018-10-25}}</ref>

135.180.198.136: /* Hugin algorithm */

2021-08-10T22:19:23Z

Hugin algorithm

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	*Propagate the probabilities along the junction tree (via [[belief propagation]])		*Propagate the probabilities along the junction tree (via [[belief propagation]])

	Note that this last step is inefficient for graphs of large [[treewidth]]. Computing the messages to pass between supernodes involves doing exact marginalization over the variables in both supernodes. Performing this algorithm for a graph with treewidth k will thus have at least one computation which takes time exponential in k. It is a [[~~Message~~ ~~passing in computer clusters~~\|message passing]] algorithm.<ref name=":2">{{Cite web\|url=http://www.gatsby.ucl.ac.uk/teaching/courses/ml1-2007/lect5-handout.pdf\|title=Recap on Graphical Models}}</ref> The Hugin algorithm takes fewer [[computation]]s to find a solution compared to Shafer-Shenoy.		Note that this last step is inefficient for graphs of large [[treewidth]]. Computing the messages to pass between supernodes involves doing exact marginalization over the variables in both supernodes. Performing this algorithm for a graph with treewidth k will thus have at least one computation which takes time exponential in k. It is a [[belief propagation\|message passing]] algorithm.<ref name=":2">{{Cite web\|url=http://www.gatsby.ucl.ac.uk/teaching/courses/ml1-2007/lect5-handout.pdf\|title=Recap on Graphical Models}}</ref> The Hugin algorithm takes fewer [[computation]]s to find a solution compared to Shafer-Shenoy.

	===Shafer-Shenoy algorithm===		===Shafer-Shenoy algorithm===

← Previous revision		Revision as of 07:56, 10 November 2023
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	* Multiple recursions of the Shafer-Shenoy algorithm results in Hugin algorithm<ref name=":3">{{Cite web\|url=https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-438-algorithms-for-inference-fall-2014/lecture-notes/MIT6_438F14_Lec14.pdf\|title=Algorithms\|date=2014\|website=Massachusetts Institute of Technology}}</ref>		* Multiple recursions of the Shafer-Shenoy algorithm results in Hugin algorithm<ref name=":3">{{Cite web\|url=https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-438-algorithms-for-inference-fall-2014/lecture-notes/MIT6_438F14_Lec14.pdf\|title=Algorithms\|date=2014\|website=Massachusetts Institute of Technology}}</ref>
	* Found by the [[Message passing in computer clusters\|message passing]] equation<ref name=":3" />		* Found by the [[Message passing in computer clusters\|message passing]] equation<ref name=":3" />
	*[[~~Separatrix~~ ~~(mathematics)~~\|Separator]] potentials are not stored<ref>{{Cite web\|url=https://cs.nyu.edu/~roweis/csc412-2004/notes/lec20x.pdf\|title=Hugin Inference Algorithm\|last=Roweis\|first=Sam\|date=2004\|website=NYU}}</ref>		*[[Vertex separator\|Separator]] potentials are not stored<ref>{{Cite web\|url=https://cs.nyu.edu/~roweis/csc412-2004/notes/lec20x.pdf\|title=Hugin Inference Algorithm\|last=Roweis\|first=Sam\|date=2004\|website=NYU}}</ref>

	The Shafer-Shenoy [[algorithm]] is the [[Sum-product algorithm\|sum product]] of a junction tree.<ref>{{Cite web\|url=https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-438-algorithms-for-inference-fall-2014/recitations/MIT6_438F14_rec8.pdf\|title=Algorithms for Inference\|date=2014\|website=Massachusetts Institute of Technology}}</ref> It is used because it runs programs and queries more efficiently than the Hugin algorithm. The algorithm makes calculations for conditionals for [[belief functions]] possible.<ref name=":02">{{cite arXiv\|last=Kłopotek\|first=Mieczysław A.\|date=2018-06-06\|title=Dempsterian-Shaferian Belief Network From Data\|eprint=1806.02373\|class=cs.AI}}</ref> [[Joint distributions]] are needed to make local computations happen.<ref name=":02" />		The Shafer-Shenoy [[algorithm]] is the [[Sum-product algorithm\|sum product]] of a junction tree.<ref>{{Cite web\|url=https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-438-algorithms-for-inference-fall-2014/recitations/MIT6_438F14_rec8.pdf\|title=Algorithms for Inference\|date=2014\|website=Massachusetts Institute of Technology}}</ref> It is used because it runs programs and queries more efficiently than the Hugin algorithm. The algorithm makes calculations for conditionals for [[belief functions]] possible.<ref name=":02">{{cite arXiv\|last=Kłopotek\|first=Mieczysław A.\|date=2018-06-06\|title=Dempsterian-Shaferian Belief Network From Data\|eprint=1806.02373\|class=cs.AI}}</ref> [[Joint distributions]] are needed to make local computations happen.<ref name=":02" />