Multilevel Functional Principal Component Analysis for High-Dimensional Data

We propose fast and scalable statistical methods for the analysis of hundreds or thousands of high dimensional vectors observed at multiple visits. The proposed inferential methods do not require loading the entire data set at once in the computer memory and instead use only sequential access to data. This allows deployment of our methodology on low-resource computers where computations can be done in minutes on extremely large data sets. Our methods are motivated by and applied to a study where hundreds of subjects were scanned using Magnetic Resonance Imaging (MRI) at two visits roughly five years apart. The original data possesses over ten billion measurements. The approach can be applied to any type of study where data can be unfolded into a long vector including densely observed functions and images. Supplemental materials are provided with source code for simulations, some technical details and proofs, and additional imaging results of the brain study.