20.500.12556/RUL-150823 Pogojna neodvisnost v jeziku algebre delo diplomskega seminarja Conditional independence in the language of algebra Glavne ugotovitve dela diplomskega seminarja so osredotočene na obravnavo pogojne neodvisnosti v jeziku algebre. Ugotovimo, kako izjave o pogojni neodvisnosti omejujejo porazdelitve in gostote. Predstavimo ideale in raznoterosti in nekatere izreke in ugotovitve, povezane z njimi. Na podlagi izrekov o ničlah se vzpostavi povezavo med ideali in algebrskimi raznoterostmi. Z idealom pogojne neodvisnosti lahko lažje predstavimo omejitve pogojne neodvisnosti. Iščemo raznoterost ideala pogojne neodvisnosti. Prikazana je praktična uporabnost primarnega razcepa, ki omogoča razpad idealov na primarne ideale. Spoznamo tudi binomske ideale, ki so zaradi svojih lastnosti pomembni za primarni razcep ideala pogojne neodvisnosti. Ogledamo si tudi primer primarnega razcepa za paroma robno neodvisne slučajne spremenljivke z uvedbo linearno zamenjanih koordinat. The main topic of the graduation seminar is the treatment of conditional independence in the language of algebra. We find out how conditional independence statements constrain distributions and densities. We present ideals and varieties and some theorems and observations related to them. A link between ideals and algebraic varieties is established on the basis of the Nullstelensatz. The ideal of conditional independence can be used to better represent the restrictions of conditional independence. We are looking for the variety of the conditional independence ideal. The practical utility of a primary decomposition is shown, which allows ideals to be decomposed into primary ideals. We learn about binomial ideals, which are important for the primary decomposition in our case because of their properties. We also look at the case of primary decomposition for pairwise independent random variables by introducing a linear coordinate substitution. pogojna neodvisnost ideal primarni ideal raznoterost primarni razcep izrek o ničlah conditional independence ideal primary ideal variety primary decomposition nullstellensatz true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2023-09-24 07:16:21 2023-09-24 07:16:23 2024-05-29 09:52:02 0000-00-00 00:00:00 2023 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512 136708 165583619 9815.pdf 9815.pdf 1 DFF0B76E6D7ECC04C4B856E1E3FDDF31 32b85355bb8a471161ea218026cb5833653a0a243c84735eee081d28dbb58547 844dfd2f-5a99-11ee-baf2-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=175637 Fakulteta za matematiko in fiziko 0 0 0