0442412 20240103205858.420150415235959.9 000348581700002 84920998684 10.1080/03081079.2014.934370 24 s. P cav_un_epca*02567940308-1079441 (2015)2-25Taylor & Francis multidimensional distribution conditional independence composition semigraphoid properties running intersection property cav_un_auth*0101118 Jiroušek Radim Matematická teorie rozhodování Department of Decision Making Theory MTR MTR UTIA-B Department of Decision Making Theory 50 Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0216188 Kratochvíl Václav Matematická teorie rozhodování Department of Decision Making Theory MTR MTR UTIA-B Department of Decision Making Theory 50 Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2015/MTR/jirousek-0442412.pdf GA13-20012S GA ČR cav_un_auth*0292670 GAP403/12/2175 GA ČR CZ cav_un_auth*0284585 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. 2016 BA 2 RVO:67985556 http://hdl.handle.net/11104/0246065 cav_un_auth*0295073 VŠE Vysoká škola ekonomická v Praze CZ Praha 3 S COMPUTERSCIENCE.THEORY&METHODS 1.244 0.302 999.9 0.00105 0.326 949 0.758 Q1 1.452 53 Q1 23.676 78.6 Q4 Q2 78.571 2015 84920998684 SCOPUS 000348581700002 WOS cav_un_epca*0256794 International Journal of General Systems 0308-1079 1563-5104 Roč. 44 č. 1 2015 2 25 Taylor & Francis