Matematičko modeliranje konsenzusa u informacijskoj geometriji

undergraduate thesis

• Title (english): Mathematical modelling of consensus in information geometry
• Author: Ivan Bukač
• Mentor: Mario Bukal (mentor)
• Committee member: Mario Bukal (predsjednik povjerenstva)
• Committee member: Lana Horvat Dmitrović (član povjerenstva)
• Committee member: Ana Žgaljić Keko (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2022-07-07, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing

Abstract

Konsenzus između skupine agenata matematički modeliramo kao sustav običnih diferencijalnih jednadžbi u kojem svaka jednadžba opisuje dinamiku pojedinog agenta i njegovu interakciju s ostalim agentima. Cilj takvog sustava jednadžbi je postignuti dogovor tj. konsenzus između agenata. U informacijskog geometriji, stanje sustava opisujemo pomoću parametara parametarskih distribucija. U ovom radu analizirani su modeli konsenzusa u prostoru parametara eksponencijalnih familija. Za linearne simetrične modele pokazano je da konvergiraju ka konsenzusu koji je jednak centru mase početnih stanja te je jednak baricentru u prostoru dualnih parametara. Numeričke simulacije provedene su za linearne i nelinearne modele na primjeru von Misesovih distribucija.

Abstract (english)

Consensus between a group of agents is mathematically modeled as a system of ordinary differential equations in which each equation describes the dynamics of an individual agent and its interaction with other agents. The goal of such a system of equations is to reach an agreement, i.e. consensus between agents. In information geometry, the state of a system is described using parameters of parametric distributions. In this thesis, consensus models in the space of parameters of exponential families are analyzed. Linear symmetric models have been shown to converge toward a consensus equal to the center of mass of the initial states, which is also equal to the barycentre in the space of dual parameters. Numerical simulations were performed for linear and nonlinear models on the example of von Mises distributions.

• Keywords: modeli konsenzusa; informacijska geometrija; matematičko modeliranje; von Mises-Fisherova razdioba; eksponencijalne familije; baricentar
• Keywords (english): consensus models; information geometry; mathematical modeling; von Mises-Fisher distribution; exponentional families; barycentre
• Language: croatian
• URN:NBN: urn:nbn:hr:168:705714
• 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: 2023-01-15 09:52:08