About: On open questions in the geometric approach to structural learning Bayesian nets

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An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	The basic idea of an algebraic approach to learning a Bayesian network (BN) structure is to represent it by a certain uniquely determined vector, called the standard imset. In a recent paper, it was shown that the set of standard imsets is the set of vertices of a certain polytope and natural geometric neighborhood for standard imsets, and, consequently, for BN structures, was introduced. The new geometric view led to a series of open mathematical questions. In this paper, we try to answer some of them. First, we introduce a class of necessary linear constraints on standard imsets and formulate a conjecture that these constraints characterize the polytope. The conjecture has been confirmed in the case of (at most) 4 variables. Second, we confirm a former hypothesis by Raymond Hemmecke that the only lattice points within the polytope are standard imsets. Third, we give a partial analysis of the geometric neighborhood in the case of 4 variables. The basic idea of an algebraic approach to learning a Bayesian network (BN) structure is to represent it by a certain uniquely determined vector, called the standard imset. In a recent paper, it was shown that the set of standard imsets is the set of vertices of a certain polytope and natural geometric neighborhood for standard imsets, and, consequently, for BN structures, was introduced. The new geometric view led to a series of open mathematical questions. In this paper, we try to answer some of them. First, we introduce a class of necessary linear constraints on standard imsets and formulate a conjecture that these constraints characterize the polytope. The conjecture has been confirmed in the case of (at most) 4 variables. Second, we confirm a former hypothesis by Raymond Hemmecke that the only lattice points within the polytope are standard imsets. Third, we give a partial analysis of the geometric neighborhood in the case of 4 variables. (en)
Title	On open questions in the geometric approach to structural learning Bayesian nets On open questions in the geometric approach to structural learning Bayesian nets (en)
skos:prefLabel	On open questions in the geometric approach to structural learning Bayesian nets On open questions in the geometric approach to structural learning Bayesian nets (en)
skos:notation	RIV/67985556:_____/11:00358907!RIV12-AV0-67985556
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(1M0572), P(GA201/08/0539), P(GEICC/08/E010), Z(AV0Z10750506)
http://linked.open...iv/cisloPeriodika	5
http://linked.open...vai/riv/dodaniDat	2012
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	218090
http://linked.open...ai/riv/idVysledku	RIV/67985556:_____/11:00358907
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	structural learning Bayesian nets; standard imset; polytope; geometric neighborhood; differential imset (en)
http://linked.open.../riv/klicoveSlovo	differential imset geometric neighborhood standard imset structural learning Bayesian nets polytope
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[6E2B8D266B82]
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	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Conditional independence structures: graphical and algebraic approaches Data, algorithms, decision making The logic of causal and probabilistic reasoning in uncertain environments
http://linked.open...UplatneniVysledku	2011
http://linked.open...v/svazekPeriodika	52
http://linked.open...iv/tvurceVysledku	Studený, Milan Vomlel, Jiří
http://linked.open...ain/vavai/riv/wos	000290426100006
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)
http://bibframe.org/vocab/doi	10.1016/j.ijar.2010.09.004

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