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A geometric view on learning Bayesian network structures
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SYSNO ASEP 0342804 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title A geometric view on learning Bayesian network structures Author(s) Studený, Milan (UTIA-B) RID, ORCID
Vomlel, Jiří (UTIA-B) RID, ORCID
Hemmecke, R. (DE)Source Title International Journal of Approximate Reasoning. - : Elsevier - ISSN 0888-613X
Roč. 51, č. 5 (2010), s. 578-586Number of pages 14 s. Action PGM 2008 Language eng - English Country US - United States Keywords learning Bayesian networks ; standard imset ; inclusion neighborhood ; geometric neighborhood ; GES algorithm Subject RIV BA - General Mathematics R&D Projects IAA100750603 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) 1M0572 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) GA201/08/0539 GA ČR - Czech Science Foundation (CSF) CEZ AV0Z10750506 - UTIA-B (2005-2011) UT WOS 000278692300009 EID SCOPUS 77955230142 DOI 10.1016/j.ijar.2010.01.014 Annotation 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. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2011
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