0375138 20240103200703.220120302235959.9 Praha Czech Technical University 2012 118 s. WWW compositional model probability model conditional independence cav_un_auth*0216188 Kratochvíl Václav Matematická teorie rozhodování Department of Decision Making Theory MTR MTR UTIA-B Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2012/MTR/kratochvil-probabilistc compositional models solution of an equivalence problem.pdf 1M0572 GA MŠk cav_un_auth*0001814 2C06019 GA MŠk CZ cav_un_auth*0216518 GA201/09/1891 GA ČR cav_un_auth*0253175 GEICC/08/E010 GA ČR cav_un_auth*0241637 CEZ:AV0Z10750506 An integral part of the work with multidimensional probabilistic models, and in particular their learning, is the perfect knowledge of the conditional independence relations of the model. The knowledge of conditional independence relations is understood here as a list of conditional independence relations valid for the model and induced by its structure. However, the representation these relations by such a structure is imperfect - two or more structures may represent the same independence relations - they are equivalent. The equivalence problem can be summed up in the following three questions: (i) how can we recognize whether two structures represent the same set of independence relations; (ii) how can we transform any one structure into another equivalent one in terms of some elementary operations; and (iii) can we generate all structures equivalent with a given one? This thesis presents the complete solution to equivalence problem. We illustrated its usage and, above that, we found a unique representative of a class of equivalent structures. 2012 BA 24.02.2011 Ph.D. Ústav teorie informace a automatizace AV ČR Pod Vodárenskou věží 4, 18202 Praha 8 2011 1 http://hdl.handle.net/11104/0207877 2012 2012 Praha Czech Technical University