Bayesove neuronske mreže

master's thesis

• Title (english): Bayesian neural networks
• Author: Joško Kristić
• Mentor: Matej Mihelčić (mentor)
• Committee member: Matej Mihelčić (predsjednik povjerenstva)
• Committee member: Goran Igaly (član povjerenstva)
• Committee member: Zvonimir Bujanović (član povjerenstva)
• Committee member: Marko Horvat (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2025-02-17, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics; Probability Theory and Statistics

Abstract

U ovom diplomskom radu obrađena je tema Bayesovih neuronskih mreža, koje predstavljaju spoj standardnih neuronskih mreža i Bayesovske statistike. U svrhu razumijevanja Bayesovih neuronskih mreža obrađuju se teme klasičnih neuronskih mreža i Bayesovskog zaključivanja, s naglaskom na Bayesov teorem te priorne i posteriorne distribucije. Detaljno se analizira struktura i razlike Bayesovih neuronskih mreža u odnosu na klasične, s fokusom na metode treniranja poput varijacijskog zaključivanja i... More Monte Carlo metoda. Mogućnost kvantifikacije neizvjesnosti Bayesovih neuronskih mreža prezentira se kroz uvođenje vrsta neizvjesnosti i njihove teorijske podloge. Za kraj teorijskog dijela, detaljno se analizira problem pretreniranosti u kontekstu strojnog učenja te metode kojima klasične i Bayesove neuronske mreže njemu pristupaju. U eksperimentalnom dijelu, na stvarnim skupovima podataka implementiraju se modeli klasičnih i Bayesovih neuronskih mreža. Kroz rezultate eksperimentalnog dijela pokazuju se mogućnosti Bayesovih neuronskih mreža i prednosti u odnosu na klasične. Less

Abstract (english)

This thesis explores the topic of Bayesian neural networks, which represent a combination of standard neural networks and Bayesian statistics. To facilitate an understanding of Bayesian neural networks, the concepts of classical neural networks and Bayesian inference are discussed, with an emphasis on Bayes' theorem and prior and posterior distributions. The structure and differences of Bayesian neural networks compared to classical ones are analyzed in detail, focusing on training... More methods such as variational inference and Monte Carlo methods. The ability of Bayesian neural networks to quantify uncertainty is presented through the introduction of types of uncertainty and their theoretical foundations. The theoretical section concludes with a detailed examination of the problem of overfitting in the context of machine learning and the methods used by classical and Bayesian neural networks to address it. In the experimental section, models of classical and Bayesian neural networks are implemented on real datasets. The results of the experimental section demonstrate the capabilities of Bayesian neural networks and their advantages over classical neural networks. Less

• Keywords: bayes; neuronske; mreže; strojno; učenje; statistika; pretreniranje; varijacijsko; zaključivanje
• Keywords (english): bayes; neural; networks; machine; learning; statistics; overfitting; variational; inference
• Language: croatian
• URN:NBN: urn:nbn:hr:217:948790
• 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: 2025-01-27 21:05:05