Motivated by scientific questions about the brain, this dissertation focuses on the development of statistical and machine learning methods for complex, multi-modal, and high-dimensional data such as images, networks, and functions. Chapter 2 introduces a fully automated pipeline for identifying severe brain swelling in brain images from low-field magnetic resonance imaging (MRI), involving a segmentation algorithm designed for low field, and the translation of radiological diagnostic criteria into image-based biomarkers of brain swelling in the context of cerebral malaria. Chapter 3 proposes a statistical framework, Conditional Correlation Models with Association Size (CoCoA), that maps the conditional correlation between two coupled outcomes to other variables that can alter the strength and direction of that correlation. We then apply CoCoA to understand the speed-accuracy trade-off in tests of complex reasoning. Chapter 4 proposes a supervised curve alignment method, Regression and Alignment for Functional Data and Network Topology (RAFT). In brain network data, RAFT allows us to relate variations in the mesoscale topology of brain connections to changes in executive function during adolescence. These new statistical methods are purpose-built for the high-dimensional and complex data types often encountered in scientific studies, and they have the potential to improve the interpretability, efficiency, and reproducibility of these studies.