Phase-Aware Federated Deep Neural Network Classification for Heterogeneous Functional Data

Music City Center 

Multi-stage neuro–imaging studies such as the Alzheimer's Disease Neuroimaging Initiative (ADNI) release data in phased cohorts that differ in scanner hardware, sampling frames, and population mix, yielding heterogeneous, high‑dimensional functional observations. Deep neural networks (DNNs) can capture the resulting non‑linear decision boundaries, but joint training is often infeasible owing to privacy constraints, phase‑specific label scarcity, and limits on storing petabyte‑scale archives. We propose a sequential distributed‑learning framework that trains a DNN classifier across K heterogeneous agents without co‑locating raw functional data. The learner visits each agent once, updates parameters locally, discards the data, and transfers only compressed weights; an adaptive, sequential gradient‑weighting strategy progressively mitigates covariate and label shift to optimize classification accuracy on the target agent, while an embedded functional feature selector pinpoints informative functional covariates. We establish minimax‑optimal excess‑risk bounds, prove selection consistency, and identify a sharp phase‑transition threshold that governs learnability for sparsely observed functional data. Simulations and an ADNI case study on three‑year MCI‑to‑AD conversion show that the method matches the accuracy of a centralized DNN, recovers key brain regions, and reduces memory and communication costs by an order of magnitude, providing a scalable, privacy‑preserving solution for heterogeneous functional data analysis.

Functional data analysis


Deep neural network classifier


Variable selection