Kompleksnost skrivenih Markovljevih modela

master's thesis

• Author: Tea Horvatek
• Mentor: Pavle Goldstein (mentor)
• Committee member: Pavle Goldstein (predsjednik povjerenstva)
• Committee member: Zoran Vondraček (član povjerenstva)
• Committee member: Željka Milin-Šipuš (član povjerenstva)
• Committee member: Sonja Štimac (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2018-02-01, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu bavili smo se analizom skrivenih Markovljevih modela. Dana je njihova formalna definicija te opisani neki algoritmi za njihovu analizu. Algoritme smo implementirali u programskom jeziku Python te primijenili na modelu nepoštene kockarnice s 32-stranim ``kockama". Prikazano je nekoliko poznatih statističkih metoda za odabir najboljeg modela, međutim, nijedna nije dala zadovoljavajući rezultat pri primjeni na procjenu kompleksnosti skrivenih Markovljevih modela. Zato u radu predlažemo novi kriterij, koji daje bolje rezultate.

Abstract (english)

This thesis is concerned with analysis of hidden Markov models. We give a formal definition of an HMM and describe several algorithms used in their analysis. We implement these algorithms in Python and show their application on an occasionally dishonest casino model with 32-sided “cubes”. We describe several known statistical methods for choosing the best model. However, none give satisfying results when used to assess the complexity of given hidden Markov model. Therefore, we propose a new criterion which gives better results.

• Keywords: skriveni Markovljevi modeli; HMM; Python; model nepoštene kockarnice
• Keywords (english): hidden Markov models; HMM; Python; occasionally dishonest casino model
• Language: croatian
• URN:NBN: urn:nbn:hr:217:619343
• Study programme: Title: Finance and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2018-11-23 14:00:59