# Bibliography

Journal Article

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

,

**: **International Journal of Approximate Reasoning vol.52, 5 (2011), p. 627-640

**: **Workshop on Uncertainty Processing WUPES'09 /8./,
(Liblice, CZ, 19.09.2009-23.09.2009)

**: ** CEZ:AV0Z10750506

**: **1M0572, GA MŠk,
GA201/08/0539, GA ČR,
2C06019, GA MŠk,
GEICC/08/E010, GA ČR

**: **structural learning Bayesian nets,
standard imset,
polytope,
geometric neighborhood,
differential imset

**: **http://library.utia.cas.cz/separaty/2011/MTR/studeny-0358907.pdf

**(eng): **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.

**: **BA