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A geometric view on learning Bayesian network structures
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SYSNO ASEP 0342804 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název A geometric view on learning Bayesian network structures Tvůrce(i) Studený, Milan (UTIA-B) RID, ORCID
Vomlel, Jiří (UTIA-B) RID, ORCID
Hemmecke, R. (DE)Zdroj.dok. International Journal of Approximate Reasoning. - : Elsevier - ISSN 0888-613X
Roč. 51, č. 5 (2010), s. 578-586Poč.str. 14 s. Akce PGM 2008 Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova learning Bayesian networks ; standard imset ; inclusion neighborhood ; geometric neighborhood ; GES algorithm Vědní obor RIV BA - Obecná matematika CEP IAA100750603 GA AV ČR - Akademie věd 1M0572 GA MŠMT - Ministerstvo školství, mládeže a tělovýchovy GA201/08/0539 GA ČR - Grantová agentura ČR CEZ AV0Z10750506 - UTIA-B (2005-2011) UT WOS 000278692300009 EID SCOPUS 77955230142 DOI 10.1016/j.ijar.2010.01.014 Anotace 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" from a perfectly Markovian distribution. Pracoviště Ústav teorie informace a automatizace Kontakt Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Rok sběru 2011
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