Scalable Machine Learning Methods for Massive Biomedical Data Analysis

Modern data acquisition techniques have enabled biomedical researchers to collect and analyze datasets of substantial size and complexity. The massive size of these datasets allows us to comprehensively study the biological system of interest at an unprecedented level of detail, which may lead to the discovery of clinically relevant biomarkers. Nonetheless, the dimensionality of these datasets presents critical computational and statistical challenges, as traditional statistical methods break down when the number of predictors dominates the number of observations, a setting frequently encountered in biomedical data analysis. This difficulty is compounded by the fact that biological data tend to be noisy and often possess complex correlation patterns among the predictors. The central goal of this dissertation is to develop a computationally tractable machine learning framework that allows us to extract scientifically meaningful information from these massive and highly complex biomedical datasets. We motivate the scope of our study by considering two important problems with clinical relevance: (1) uncertainty analysis for biomedical image registration, and (2) psychiatric disease prediction based on functional connectomes, which are high dimensional correlation maps generated from resting state functional MRI.