Foundations of compositional models: structural properties

0442412 - ÚTIA 2016 RIV GB eng J - Journal Article
Jiroušek, Radim - Kratochvíl, Václav
Foundations of compositional models: structural properties.
International Journal of General Systems. Roč. 44, č. 1 (2015), s. 2-25. ISSN 0308-1079. E-ISSN 1563-5104
R&D Projects: GA ČR GA13-20012S
Grant - others:GA ČR(CZ) GAP403/12/2175
Program: GA
Institutional support: RVO:67985556
Keywords : multidimensional distribution * conditional independence * composition * semigraphoid properties * running intersection property
Subject RIV: BA - General Mathematics
Impact factor: 1.677, year: 2015
http://library.utia.cas.cz/separaty/2015/MTR/jirousek-0442412.pdf

The paper is a follow-up of [R.J.: Foundations of compositional model theory. IJGS, 40(2011): 623–678], where basic properties of compositional models, as one of the approaches to multidimensional probability distributions representation and processing, were introduced. In fact, it is an algebraic alternative to graphical models, which does not use graphs to represent conditional independence statements. Here, these statements are encoded in a sequence of distributions to which an operator of composition – the key element of this theory – is applied in order to assemble a multidimensional model from its low-dimensional parts. In this paper, we show a way to read conditional independence relations, and to solve related topics, above all the so-called equivalence problem, i.e. the problem of recognizing whether two different structures induce the same system of conditional independence relations.
Permanent Link: http://hdl.handle.net/11104/0246065