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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F11%3A00358907" target="_blank" >RIV/67985556:_____/11:00358907 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.ijar.2010.09.004" target="_blank" >http://dx.doi.org/10.1016/j.ijar.2010.09.004</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ijar.2010.09.004" target="_blank" >10.1016/j.ijar.2010.09.004</a>

Result language
angličtina
Original language name
On open questions in the geometric approach to structural learning Bayesian nets
Original language 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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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