0358907 20240103195114.120110510235959.9 000290426100006 10.1016/j.ijar.2010.09.004 14 s. cav_un_epca*02567740888-613X525 (2011)627-640Elsevier structural learning Bayesian nets standard imset polytope geometric neighborhood differential imset cav_un_auth*0101202 Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory Studený Milan UTIA-B Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0101228 Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory Vomlel Jiří UTIA-B Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2011/MTR/studeny-0358907.pdf cav_un_auth*0001814 1M0572 GA MŠk CZ cav_un_auth*0239648 GA201/08/0539 GA ČR cav_un_auth*0216518 2C06019 GA MŠk CZ cav_un_auth*0241637 GEICC/08/E010 GA ČR CEZ:AV0Z10750506 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. cav_un_auth*0271586 Workshop on Uncertainty Processing WUPES'09 /8./ 19.09.2009-23.09.2009 Liblice CZ BA 2012 http://hdl.handle.net/11104/0196817 COMPUTERSCIENCEARTIFICIALINTELLIGENCE 2.155 0.293 4.7 0.00594 0.759 1638 92 1.703 Q1 70.492 76.126 Q2 Q1* 2011 000290426100006 WOS cav_un_epca*0256774 International Journal of Approximate Reasoning 0888-613X 1873-4731 Roč. 52 č. 5 2011 627 640 Elsevier