Regresija z Gaussovimi procesi : delo diplomskega seminarja

Kovačič, Sara (author), Peperko, Aljoša (mentor)

V delu je predstavljena regresija z Gaussovimi procesi iz vidika uteženega prostora in s pogledom iz prostora funkcij. Ponovljenih je nekaj osnov Bayesove statistike in lastnosti normalne porazdelitve. Za namene modeliranja in strojnega učenja je predstavljena tudi teorija učenja modela. Ker so z Gaussovimi procesi tesno povezane kovariančne funkcije, je predstavljenih nekaj najpogostejših kovariančnih funkcij. V empiričnem delu naloge sta opisana Pythonova knjižnica za strojno učenje Scikit-learn in primer regresije z Gaussovimi procesi na rezultatih nacionalnega preverjanja znanja za osnovnošolce iz leta 2019.

• Language: Slovenian
• Keywords: Gaussov proces, kovariančna funkcija, regresija, strojno učenje
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2019
• PID: 20.500.12556/RUL-110969
• UDC: 519.2
• COBISS.SI-ID: 18737241
• Publication date in RUL: 21.09.2019

Secondary language

• Language: English
• Title: Gaussian process regression

Abstract

The thesis presents the Gaussian process regression from the weight space view and the function space view. It examines some of Bayesian statistics and normal distribution properties. For modeling and machine learning purposes the model learning theory is also presented. Since covariance functions are tightly connected to the Gaussian process the thesis contains a presentation of the most frequent covariance functions. The empirical part of the thesis includes a description of Python’s Scikit-learn machine learning library as well as an example of the Gaussian process regression based on the results of the 2019 national assessment of elementary school students in Slovenia.

• Keywords: Gaussian process, covariance function, regression, machine learning