Gaussian Process Regression

Thy Châu Anh Pham

Diplomová práce

Anotace:

In the Bayesian approach, the data are supplemented with additional information in the form of a prior probability distribution. The prior belief about the parameters is combined with the data's likelihood function according to Bayes theorem to yield the posterior belief about the parameters. We presenting some important issues about Bayesian statistics, multivariate normal distribution and linear model. Then the posterior and posterior predictive distribution for linear regression model is derived. Some visual examples about the Bayesian linear model are also presented. Finally, the connection between standard Bayesian treatment of linear models and Gaussian process regression is discussed.

Abstract:

In the Bayesian approach, the data are supplemented with additional information in the form of a prior probability distribution. The prior belief about the parameters is combined with the data's likelihood function according to Bayes theorem to yield the posterior belief about the parameters. We presenting some important issues about Bayesian statistics, multivariate normal distribution and linear model. Then the posterior and posterior predictive distribution for linear regression model is derived. Some visual examples about the Bayesian linear model are also presented. Finally, the connection between standard Bayesian treatment of linear models and Gaussian process regression is discussed.

Klíčová slova

{Bayesian statistic, Gaussian process, multivariate normal distribution, linear regresssion

Keywords

{Bayesian statistic, Gaussian process, multivariate normal distribution, linear regresssion

Jazyk práce: angličtina

Datum vytvoření / odevzdání či podání práce: 30. 4. 2019

Obhajoba závěrečné práce

• Obhajoba proběhla 29. 5. 2019
• Vedoucí: Jan Kracík
• Oponent: Simona Domesová

VŠB - Technická univerzita Ostrava

Fakulta elektrotechniky a informatiky

Magisterský studijní program / obor:
Informační a komunikační technologie / Výpočetní matematika