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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2011

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

International Journal of Approximate Reasoning

ISSN

0888-613X

e-ISSN

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Svazek periodika

52

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

14

Strana od-do

627-640

Kód UT WoS článku

000290426100006

EID výsledku v databázi Scopus

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