Statistical Inference on Large-scale and Complex Data via Gaussian Process

Abstract

Recent technological advancements have generated vast amounts of complex data in various fields, including biomedical sciences such as neuroimages, electronic health records, and electroencephalogram (EEG) signals obtained from brain computer interface (BCI) systems. However, the analysis of such data presents significant challenges due to its high dimensionality, spatial or temporal resolution, correlation structure, and heterogeneity. Gaussian Processes (GPs) have emerged as a flexible tool for Bayesian nonparametrics and machine learning, enabling the modeling of functional and dependent data over time and space. The nonparametric flexibility and high interpretability of GPs have led to their success in numerous applications. Nevertheless, existing GP models and methods are inadequate in addressing new questions that arise in analyzing large-scale and complex data. This dissertation aims to fill this gap by developing novel GP-based models and proposing efficient posterior computation algorithms using GP priors for the statistical analysis of large-scale and complex data, with a focus on biomedical applications such as brain imaging and EEG-BCI data analysis.