About: A geometric view on learning Bayesian network structures

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Basic idea of an algebraic approach to learning Bayesian network (BN) structures is to represent every BN structure by a certain (uniquely determined) vector, called a standard imset. The main result of the paper is that the set of standard imsets is the set of vertices of a certain polytope. Motivated by the geometric view, we introduce the concept of the geometric neighborhood for standard imsets, and, consequently, for BN structures. Then we show that it always includes the inclusion neighborhood}, which was introduced earlier in connection with the GES algorithm. The third result is that the global optimum of an affine function over the polytope coincides with the local optimum relative to the geometric neighborhood. The geometric neighborhood in the case of three variables is described and shown to differ from the inclusion neighborhood. This leads to a simple example of the failure of the GES algorithm if data are not ``generated%22 from a perfectly Markovian distribution. Basic idea of an algebraic approach to learning Bayesian network (BN) structures is to represent every BN structure by a certain (uniquely determined) vector, called a standard imset. The main result of the paper is that the set of standard imsets is the set of vertices of a certain polytope. Motivated by the geometric view, we introduce the concept of the geometric neighborhood for standard imsets, and, consequently, for BN structures. Then we show that it always includes the inclusion neighborhood}, which was introduced earlier in connection with the GES algorithm. The third result is that the global optimum of an affine function over the polytope coincides with the local optimum relative to the geometric neighborhood. The geometric neighborhood in the case of three variables is described and shown to differ from the inclusion neighborhood. This leads to a simple example of the failure of the GES algorithm if data are not ``generated%22 from a perfectly Markovian distribution. (en)
Title	A geometric view on learning Bayesian network structures A geometric view on learning Bayesian network structures (en)
skos:prefLabel	A geometric view on learning Bayesian network structures A geometric view on learning Bayesian network structures (en)
skos:notation	RIV/67985556:_____/10:00342804!RIV11-MSM-67985556
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(1M0572), P(2C06019), P(GA201/08/0539), P(IAA100750603), Z(AV0Z10750506)
http://linked.open...iv/cisloPeriodika	5
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Vomlel, Jiří Studený, Milan
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav teorie informace a automatizace AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	244642
http://linked.open...ai/riv/idVysledku	RIV/67985556:_____/10:00342804
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	learning Bayesian networks; standard imset; inclusion neighborhood; geometric neighborhood; GES algorithm (en)
http://linked.open.../riv/klicoveSlovo	geometric neighborhood standard imset GES algorithm inclusion neighborhood learning Bayesian networks
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[6655BE6A8307]
http://linked.open...i/riv/nazevZdroje	International Journal of Approximate Reasoning
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Conditional independence structures: graphical and algebraic approaches Data, algorithms, decision making (Medical) Knowledge Acquisition and Modelling Information geomerty of multidimensional models in statistics and artificial intelligence.
http://linked.open...UplatneniVysledku	2010
http://linked.open...v/svazekPeriodika	51
http://linked.open...iv/tvurceVysledku	Studený, Milan Vomlel, Jiří Hemmecke, R.
http://linked.open...ain/vavai/riv/wos	000278692300009
http://linked.open...n/vavai/riv/zamer	Pokročilé matematické metody získávání, zpracování a využití informací a znalostí ve složitých a nedeterministických systémech
issn	0888-613X
number of pages	14 (xsd:int)
is http://linked.open...avai/riv/vysledek of	A geometric view on learning Bayesian network structures A geometric view on learning Bayesian network structures A geometric view on learning Bayesian network structures

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