Hawkesovi procesi

master's thesis

• Title (english): Hawkes processes
• Author: Luis Pich-Aguilera
• Mentor: Hrvoje Planinić (mentor)
• Committee member: Rudi Mrazović (predsjednik povjerenstva)
• Committee member: Nenad Antonić (član povjerenstva)
• Committee member: Tina Bosner (član povjerenstva)
• Committee member: Mladen Vuković (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2024-07-16, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Ovaj rad istražuje teoriju i primjenu vremenskih točkovnih procesa, s posebnim naglaskom na Poissonove i Hawkesove procese. Poissonovi procesi omogućuju modeliranje nezavisnih događaja koji se javljaju s konstantnom stopom intenziteta, dok Hawkesovi procesi imaju self-exciting svojstvo, gdje svaki događaj povećava stopu budućih događaja. U prvom dijelu rada razmatraju se osnovni pojmovi i svojstva brojećih procesa, te se uvode homogeni i nehomogeni Poissonovi procesi. Detaljno se analiziraju intenziteti tih procesa i njihova primjena u raznim područjima. Drugi dio rada posvećen je Hawkesovim procesima. Opisana je njihova struktura, uvjetna funkcija intenziteta i teorija grananja. Na kraju opisujemo simulaciju Hawkesovih procesa koristeći thinning algoritam. Treći dio rada fokusira se na jednu istaknutu primjenu Hawkesovih procesa u modeliranju širenja informacija na društvenim mrežama, s naglaskom na analizu retweet kaskada. Dizajn funkcijske jezgre, procjena parametara i predikcija popularnosti detaljno su opisani. Rezultati ovog istraživanja doprinose boljem razumijevanju strukture i dinamike događaja kroz vrijeme, te nude značajne uvide za primjenu u različitim znanstvenim i praktičnim područjima.

Abstract (english)

This thesis explores the theory and application of temporal point processes, with a special focus on Poisson and Hawkes processes. Poisson processes allow for the modeling of independent events that occur at a constant rate of intensity, while Hawkes processes introduce the concept of self-excitement, where each event increases the rate of future events. The first part of the thesis examines the basic concepts and properties of counting processes, introducing homogeneous and non-homogeneous Poisson processes. The intensities of these processes and their applications in various fields are analyzed in detail. The second part of the thesis is dedicated to Hawkes processes. Their structure, conditional intensity function, and branching theory are described. Finally the simulation of Hawkes processes using the thinning algorithm is discussed. The third part of the thesis focuses on one application of Hawkes processes in modeling the spread of information on social networks, with an emphasis on the analysis of retweet cascades, is particularly highlighted. The design of the kernel function, parameter estimation, and popularity prediction are described in detail. The results of this research contribute to a better understanding of the structure and dynamics of events over time and offer significant insights for application in various scientific and practical fields

• Keywords: vremenski točkovni procesi; Poissonovi procesi; Hawkesovi procesi
• Language: croatian
• URN:NBN: urn:nbn:hr:217:306772
• Study programme: Title: Computer Science and Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-07-24 13:07:13