Skriveni Markovljevi modeli i primjene

master's thesis

• Title (english): Hidden Markov models and applications
• Author: Tessa Bauman
• Mentor: Bojan Basrak (mentor)
• Committee member: Bojan Basrak (predsjednik povjerenstva)
• Committee member: Pavle Goldstein (član povjerenstva)
• Committee member: Snježana Lubura Strunjak (član povjerenstva)
• Committee member: Rudi Mrazović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-11-20, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu su obrađeni skriveni Markovljevi modeli s diskretnim skupom stanja i diskretnim skupom opažanja. Uvedena je formalna definicija te su zatim objašnjeni glavni problemi modela. Opisana su njihova rješenja i algoritmi pomoću kojih dolazimo do istih. Pomoću primjera nepoštenog kasina i jednostavnog primjera iz bioinformatike pokazana je inicijalizacija modela, simulacija niza opažanja te upotreba Viterbijevog i Baum- Welchovog algoritma koristeći programski jezik R. Provedena je i primjena modela za raspoznavanje razlike izmedu teksta i koda te zaključak o modelu i njegovim primjenama.

Abstract (english)

This thesis starts with an introduction to Markov Chains which is followed by a formal definition of Hidden Markov models with discrete state and discrete observation space. The three main problems and their solutions are described along with an algorithm for each. The example of Dishonest Casino and a simple bioinformatics application are used to show the model initialization, sequence simulation and usage of Viterbi and Baum- Welch algorithms in the programming language R. An application in text analysis is also showed in this thesis leading to a conclusion on Hidden Markov models and their usage

• Keywords: skriveni Markovljevi modeli; primjer nepoštenog kasina; bioinformatika; Viterbijevo algoritm; Baum- Welchovog algoritm; programski jezik R
• Keywords (english): hidden Markov models; Markov Chains; Dishonest Casino; bioinformatics; Viterbi algorithm; Baum- Welch algorithm; programming language R
• Language: croatian
• URN:NBN: urn:nbn:hr:217:731360
• 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: 2021-02-22 11:36:23