  Linkage analysis has provided valuable insights to the GWAS studies,
particularly in revealing that SNPs in linkage disequilibrium (LD) can jointly
influence disease phenotypes. However, the potential of LD network data has
often been overlooked or underutilized in the literature. In this paper, we
propose a locally adaptive structure learning algorithm (LASLA) that provides a
principled and generic framework for incorporating network data or multiple
samples of auxiliary data from related source domains; possibly in different
dimensions/structures and from diverse populations. LASLA employs a $p$-value
weighting approach, utilizing structural insights to assign data-driven weights
to individual test points. Theoretical analysis shows that LASLA can
asymptotically control FDR with independent or weakly dependent primary
statistics, and achieve higher power when the network data is informative.
Efficiency again of LASLA is illustrated through various synthetic experiments
and an application to T2D-associated SNP identification.
