Accurate prediction of lung cancer subtypes or Alzheimer's disease status is critical for early detection and prevention of the disease. Conventional prediction approaches using ultrahigh-dimensional genomic profiles or brain-wide imaging scans ignore marginally weak signals. Even though marginally weak signals by themselves are not predictive, they could exert strong prediction effects when considered in connection with the marginally strong signals. We propose a classification method which significantly improves the disease prediction accuracy by detecting and integrating the local predictive gene/brain networks. A local predictive gene/brain network contains not only marginally strong signals, but also the marginally weak signals in connection with the strong ones. The detected local predictive networks provide biological insights on how the gene/brain pathways attribute to lung cancer/AD development and progression. We applied the proposed method to the Boston Lung Cancer Study Cohort and the Alzheimer's Disease Neuroimaging Initiative (ADNI) datasets for lung cancer subtype and Alzheimer's disease status prediction.