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March 2020 Bayesian Network Marker Selection via the Thresholded Graph Laplacian Gaussian Prior
Qingpo Cai, Jian Kang, Tianwei Yu
Bayesian Anal. 15(1): 79-102 (March 2020). DOI: 10.1214/18-BA1142

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).

Citation

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Qingpo Cai. Jian Kang. Tianwei Yu. "Bayesian Network Marker Selection via the Thresholded Graph Laplacian Gaussian Prior." Bayesian Anal. 15 (1) 79 - 102, March 2020. https://doi.org/10.1214/18-BA1142

Information

Published: March 2020
First available in Project Euclid: 5 January 2019

zbMATH: 1437.62291
MathSciNet: MR4050878
Digital Object Identifier: 10.1214/18-BA1142

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Vol.15 • No. 1 • March 2020
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