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IJAR

2011

2011

The 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 the standard imset. In a recent paper (Studen´y, Vomlel, Hemmecke 2010), it was shown that the set S of standard imsets is the set of vertices (= extreme points) of a certain polytope P 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 P. 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 (= vectors having integers as components) within P are standard imsets. Third, we give a partial ...

Added |
29 Aug 2011 |

Updated |
29 Aug 2011 |

Type |
Journal |

Year |
2011 |

Where |
IJAR |

Authors |
Milan Studený, Jirí Vomlel |

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