Robust and Scalable Distributed Learning for Surface‐Based Imaging Regression with Applications to Neuroimaging

Music City Center 

High-dimensional medical imaging data are rapidly expanding, yet their complex structure and measurement errors pose significant challenges for reliable scientific discovery. We propose a robust distributed image-on-scalar Regression (R-DISR) framework that integrates spatially varying coefficient models with triangulated spherical spline smoothing via domain decomposition. This approach is designed to handle heavy-tailed noise and measurement errors while achieving near-linear computational speedup and minimizing communication overhead in distributed computing environments. We rigorously establish that the R-DISR estimators attain the same convergence rate as full-sample global estimators and derive their asymptotic distributions. Moreover, a weighted bootstrap procedure is developed to construct simultaneous confidence corridors for the spatially varying coefficient functions. Extensive simulation studies demonstrate the method's finite-sample performance, and its application to cortical surface-based functional magnetic resonance imaging data from the Human Connectome Project illustrates its effectiveness and scalability for analyzing large-scale imaging datasets.

Nonparametric Smoothing

Penalized Splines

Robust estimation

Robust Inference

Simultaneous Confidence Corridors

Triangulation 

Section on Nonparametric Statistics