Recent advances on the reduction and analysis of big and high-dimensional data

Abstract

In an era with remarkable advancements in computer engineering, computational algorithms, and mathematical modeling, data scientists are inevitably faced with the challenge of working with big and high-dimensional data. For many problems, data reduction is a necessary first step; such reduction allows for storage and portability of big data, and enables the computation of expensive downstream quantities. The next step then involves the analysis of big data -- the use of such data for modeling, inference, and prediction. This thesis presents new methods for big data reduction and analysis, with a focus on solving real-world problems in statistics, machine learning and engineering.