Auto-Encoder Enhanced Multi-Task Gaussian Process Regression for Multivariate Regression

Details

Supervisors

Van Oirbeek, Robin

Faculty

Faculté des sciences

Degree label

Master [120] en science des données, orientation statistique, à finalité spécialisée

Abstract

This master thesis aims to provide a holistic overview of Gaussian Process Regression. In fact, while widely used, understanding of Gaussian Process Regression models remains limited especially its link to the Gaussian distribution and to Bayesian Statistics. It starts by explaining the concepts related to Gaussian distribution, Gaussian Process Models and Gaussian Process Regression by linking it to Bayesian Linear Regression and Conditional Gaussian distribution. It then makes a smooth transition toward Multi-Task Gaussian Process Regression. It highlights current methods for modeling inputs and tasks covariance together. A new approach for Multi-Task Gaussian Process Regression is then proposed. The theoretical aspects of this new approach and its component are discussed. A simulated data analysis as well as a real data analysis are performed to verify theoretical findings.