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On open questions in the geometric approach to structural learning Bayesian nets
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SYSNO ASEP 0358907 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název On open questions in the geometric approach to structural learning Bayesian nets Tvůrce(i) Studený, Milan (UTIA-B) RID, ORCID
Vomlel, Jiří (UTIA-B) RID, ORCIDZdroj.dok. International Journal of Approximate Reasoning. - : Elsevier - ISSN 0888-613X
Roč. 52, č. 5 (2011), s. 627-640Poč.str. 14 s. Akce Workshop on Uncertainty Processing WUPES'09 /8./ Datum konání 19.09.2009-23.09.2009 Místo konání Liblice Země CZ - Česká republika Typ akce WRD Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova structural learning Bayesian nets ; standard imset ; polytope ; geometric neighborhood ; differential imset Vědní obor RIV BA - Obecná matematika CEP 1M0572 GA MŠMT - Ministerstvo školství, mládeže a tělovýchovy GA201/08/0539 GA ČR - Grantová agentura ČR GEICC/08/E010 GA ČR - Grantová agentura ČR CEZ AV0Z10750506 - UTIA-B (2005-2011) UT WOS 000290426100006 DOI 10.1016/j.ijar.2010.09.004 Anotace 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. Pracoviště Ústav teorie informace a automatizace Kontakt Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Rok sběru 2012
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