Bayesian Network Marker Selection via the Thresholded Graph Laplacian Gaussian Prior

Abstract

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).

Keywords: gene network; generalized linear model; network marker selection; posterior consistency; thresholded graph Laplacian Gaussian prior.

Figure 1:

An example of the graph and the corresponding correlation matrix of γ that was constructed from the inverse graph Laplacian matrix.

Figure 2:

Two types network markers in the simulated small simple networks, where true informative nodes are marked in red. In Type 1 network marker, TF and all target genes are informative nodes. In Type 2 network marker, TF and half of target genes are informative nodes.

Figure 3:

Two example modules of selected genes.