  Selecting informative nodes over large-scale networks becomes increasingly
important in many research areas. Most existing methods focus on the local
network structure and incur heavy computational costs for the large-scale
problem. In this work, we propose a novel prior model for Bayesian network
marker selection in the generalized linear model (GLM) framework: the
Thresholded Graph Laplacian Gaussian (TGLG) prior, which adopts the graph
Laplacian matrix to characterize the conditional dependence between neighboring
markers accounting for the global network structure. Under mild conditions, we
show the proposed model enjoys the posterior consistency with a diverging
number of edges and nodes in the network. We also develop a Metropolis-adjusted
Langevin algorithm (MALA) for efficient posterior computation, which is
scalable to large-scale networks. We illustrate the superiorities of the
proposed method compared with existing alternatives via extensive simulation
studies and an analysis of the breast cancer gene expression dataset in the
Cancer Genome Atlas (TCGA).
