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Publikace

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

Typ:
Článek v odborném periodiku
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Název periodika:
International Journal of Approximate Reasoning
Rok:
2011
Číslo:
5 (2011)
Strany:
627-640
ISSN:
0888-613X
Klíčová slova:
structural learning Bayesian nets, standard imset, polytope,
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.
 
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