A geometric view on learning Bayesian network structures

0342804 - ÚTIA 2011 RIV US eng J - Journal Article
Studený, Milan - Vomlel, Jiří - Hemmecke, R.
A geometric view on learning Bayesian network structures.
International Journal of Approximate Reasoning. Roč. 51, č. 5 (2010), s. 578-586. ISSN 0888-613X. E-ISSN 1873-4731.
[PGM 2008]
R&D Projects: GA AV ČR(CZ) IAA100750603; GA MŠMT(CZ) 1M0572; GA ČR GA201/08/0539
Grant - others:GA MŠk(CZ) 2C06019
Institutional research plan: CEZ:AV0Z10750506
Keywords : learning Bayesian networks * standard imset * inclusion neighborhood * geometric neighborhood * GES algorithm
Subject RIV: BA - General Mathematics
Impact factor: 1.679, year: 2010
http://library.utia.cas.cz/separaty/2010/MTR/studeny-0342804.pdf

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 a standard imset. The main result of the paper is that the set of standard imsets is the set of vertices of a certain polytope. Motivated by the geometric view, we introduce the concept of the geometric neighborhood for standard imsets, and, consequently, for BN structures. Then we show that it always includes the inclusion neighborhood}, which was introduced earlier in connection with the GES algorithm. The third result is that the global optimum of an affine function over the polytope coincides with the local optimum relative to the geometric neighborhood. The geometric neighborhood in the case of three variables is described and shown to differ from the inclusion neighborhood. This leads to a simple example of the failure of the GES algorithm if data are not ``generated" from a perfectly Markovian distribution.
Permanent Link: http://hdl.handle.net/11104/0185432