Advances in Probabilistic Graphical Models

0085219 - ÚTIA 2008 RIV DE eng M - Monography Chapter
Vomlel, Jiří - Studený, Milan
Graphical and Algebraic Representatives of Conditional Independence Models.
[Grafoví a algebraičtí reprezentanti modelů podmíněné nezávislosti.]
Advances in Probabilistic Graphical Models. Berlin Heildeberg: Springer Verlag, 2007 - (Lucas, P.; Gámez, J.; Salmerón, A.), s. 55-80. ISBN 978-3-540-68994-2
R&D Projects: GA ČR GA201/04/0393
Institutional research plan: CEZ:AV0Z10750506
Keywords : graphical models * conditional indepenence
Subject RIV: BB - Applied Statistics, Operational Research

The topic of this book chapter is conditional independence models. We review mathematical objects that are used to generate conditional independence models in the area of probabilistic reasoning. More specifically, we mention undirected graphs, acyclic directed graphs, chain graphs, and an alternative algebraic approach that uses certain integer-valued vectors, named imsets. We compare the expressive power of these objects and discuss the problem of their uniqueness. In learning Bayesian networks one meets the problem of non-unique graphical description of the respective statistical model. One way to avoid this problem is to use special chain graphs, named essential graphs. An alternative algebraic approach uses certain imsets, named standard imsets, instead. We present algorithms that make it possible to transform graphical representatives into algebraic ones and conversely. The algorithms were implemented in the R language.

Tématem této kapitoly v knize jsou gravové a algebraické modely podmíněné nezávislosti. V kapitole se konkrétně zabýváme neorientovanými a orientovanými grafy, řetězcovými grafy a alternativním algebraickým přístupem, který využívá vektory celých čísel, tak zvané imsety.
Permanent Link: http://hdl.handle.net/11104/0147780