High Dimensional Neuroimaging Data Integration and Inference

The presence of multi-block (multi-omic, multi-source) data has given rise to the field of data integration. Disciplines such as genomics, oncology, anthropology, and in particular cognitive neuroscience, offer alluring applications to any method claiming to advance the integration literature. Here, we explore and extend Data Integration via Analysis of Subspace (DIVAS), a novel integration technique. DIVAS combines new insights in angular subspace perturbation theory with recent developments in matrix signal processing and convex-concave optimization into one algorithm for exploring partially-shared structure. Contributions of this work to DIVAS include refining the optimization initialization, ensuring order agnostic behavior, generalizing the noise variance estimation, and proving a continuity result for the rotational bootstrap procedure. Exploration includes applying DIVAS to Human Connectome Project brain connectivity data. More specifically, we integrate structural and functional connectivity data alongside cognitive performance, substance use, and genetic data as part of a unified analysis. This gives rise to the important finding that genetics isthe single data modality most predictive of brain connectivity, outside of brain connectivity itself. Nearly 14\% of the variation in functional connectivity (FC) and roughly 12\% of the variation in structural connectivity (SC) is attributed to shared spaces with genetics. Moreover, investigations of shared space loadings provide interpretable associations between particular brain regions and drivers of variability. Novel Jackstraw hypothesis tests are developed for the DIVAS framework to establish statistically significant loadings. For example, in the (FC, SC, and Substance Use) subspace, these novel hypothesis tests highlight largely negative functional and structural connections suggesting the brain’s role in physiological responses to increased substance use. Our findings are validated on genetically relevant subjects not studied in the main analysis. The final chapter of this dissertation is dedicated to \textit{Moral Machine Learning}, a novel course developed and implemented at UNC. It currently satisfies the data, culture and society credit of the data science minor as well as elective credit in the statistics and analytics minor. With regard to content, statistical applications are increasingly inducing ethical considerations, which are often not able to be resolved via statistics alone. These considerations include data privacy concerns, proper interpretation of data and methods, as well as algorithmic bias. This chapter will present a subset of the developed course notes corresponding to the data privacy section of the course, a consideration that is directly relevant for any research involving human subject data. This chapter will also include a pedagogical manuscript that details how this course can be taught at other similar large research institutions. As such, the instructional methods included are designed with implementation at a large research institution in mind but are fully intended to be transferable to any setting adopting such an interdisciplinary course into its curriculum. Formative and summative assessment mechanisms will be presented alongside future directions and potential pitfalls of such a course. Motivating the proposed course is a desire to fill the comparative void in moral reasoning for statistics and data science curricula.