Algoritam maksimizacije očekivanja za eksponencijalne familije

undergraduate thesis

• Title (english): Expectation maximization algorithm for exponential families
• Author: Magda Radić
• Mentor: Mario Bukal (mentor)
• Committee member: Mario Bukal (predsjednik povjerenstva)
• Committee member: Josip Žubrinić (član povjerenstva)
• Committee member: Vlatko Crnković (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2023-07-12, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing

Abstract

U svrhu analize teksta kao usmjerenog podatka, ovaj rad daje uvod u neke pojmove iz usmjerene statistike: von Mises-Fisherovu distribuciju (vMF) i konveksnu kombinaciju von Mises-Fisherovih distribucija(moVMF). Nadalje se definiraju procjenitelji parametara vMF distribucije temeljeni na metodi najveće vjerodostojnosti. Potom se objašnjava algoritam maksmizacije očekivanja, te njegova implementacija na procjenu parametara konveksne kombinacije vMF distribucija.
Konačno, implementacija se testira na programski generiranim podacima, i na skupu podataka generiranom iz stvarnih tekstova, uz kratak osvrt na rezultate.

Abstract (english)

For the purpose of analyzing text as directional data, this paper provides an introduction to some concepts from directional statistics: von Mises-Fisher distribution (vMF) and mixture of von Mises-Fisher distributions (moVMF). Furthermore, estimators of the parameters of the vMF distribution based on the Maximum Likelihood estimation are defined. The paper then presents the Expectation-Maximization algorithm, as well as its implementation to estimation the parameters of the mixture of vMF distributions.
Finally, the implementation is tested on artificially generated data, as well as on a data set generated from real texts, with a brief overview of the results.

• Keywords: algoritam maksmizacije očekivanja; von Mises-Fisherova distribucija; algoritam k-sredina; eksponencijalne familije; usmjerena statistika
• Keywords (english): expectation maximization algorithm; von Mises-Fisher distribution; k-means algortihm; exponential families; directional statistics
• Language: croatian
• URN:NBN: urn:nbn:hr:168:499116
• Study programme: Title: Computing; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2023-10-11 10:17:02