Markovljevi modeli i primjene

master's thesis

• Title (english): Markov models and applications
• Author: Leonarda Jozinović
• Mentor: Petra Lazić (mentor)
• Committee member: Petra Lazić (predsjednik povjerenstva)
• Committee member: Snježana Lubura Strunjak (član povjerenstva)
• Committee member: Maja Resman (član povjerenstva)
• Committee member: Zoran Vondraček (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2024-02-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu napravljen je pregled četiri tipa Markovljevih modela. Opisana je struktura Markovljevih lanaca kao osnovog tipa Markovljevih procesa te je spomenut PageRank algoritam i primjena u predviđanju vremenske prognoze. Nakon toga je definirano što su skriveni Markovljevi lanci te su objašnjeni glavni problemi modela. Autorov doprinos ovoj temi je uvođenje primjera koji ilustriraju backward, forward i Viterbijev algoritam te omogućuju razumijevanje praktične primjene algoritama i tema obrađenih u radu. Navedene su i primjene u biologiji, obradi prirodnog jezika i robotici koje pokazuju važnost modela. Zatim je definiran Markovljev proces odlučivanja i dano je rješenje problema maksimizacije nagrade, a pomoću primjera pokazano je kako koristiti model za modeliranje donošenja odluka. Na kraju je dan kratak osvrt na djelomično vidljive Markovljeve procese odlučivanja.

Abstract (english)

In this paper, an overview of four types of Markov models is provided. The structure of Markov chains, as the basic type of Markov processes, is described, and the PageRank algorithm is mentioned along with its application in weather forecasting. Subsequently, hidden Markov chains are defined, and the main problems of the model are explained. The author’s contribution to this topic lies in the introduction of examples illustrating the backward, forward and Viterbi algorithms, enabling understanding of the practical application of the algorithms and topics discussed in the paper. Applications in biology, natural language processing, and robotics are also mentioned, highlighting the importance of the models. Next, the Markov decision process is defined, and a solution to the reward maximization problem is provided, demonstrating how to use the model to model decision-making through examples. Finally, a brief overview of partially observable Markov decision processes is given.

• Keywords: Markovljevi lanci; PageRank algoritam; predviđanje vremenske prognoze; Viterbijev algoritam
• Language: croatian
• URN:NBN: urn:nbn:hr:217:145616
• Study programme: Title: Mathematical Statistics; Study programme type: university; Study level: graduate; Academic / professional title: sveučilišni magistar matematike (sveučilišni magistar matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-03-13 10:28:33