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Gene Network Reconstruction using Global-Local Shrinkage Priors

Published version
Peer-reviewed

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Authors

Leday, GGR 
De Gunst, MCM 
Krogbezan, GB 
van der Vaart, AW 
van Wieringen, WN 

Abstract

Reconstructing a gene network from high-throughput molecular data is an important but challenging task, as the number of parameters to estimate easily is much larger than the sample size. A conventional remedy is to regularize or penalize the model likelihood. In network models, this is often done locally in the neighborhood of each node or gene. However, estimation of the many regularization parameters is often difficult and can result in large statistical uncertainties. In this paper we propose to combine local regularization with global shrinkage of the regularization parameters to borrow strength between genes and improve inference. We employ a simple Bayesian model with nonsparse, conjugate priors to facilitate the use of fast variational approximations to posteriors. We discuss empirical Bayes estimation of hyperparameters of the priors, and propose a novel approach to rank-based posterior thresholding. Using extensive model- and data-based simulations, we demonstrate that the proposed inference strategy outperforms popular (sparse) methods, yields more stable edges, and is more reproducible. The proposed method, termed ShrinkNet, is then applied to Glioblastoma to investigate the interactions between genes associated with patient survival.

Description

Keywords

undirected gene network, Bayesian inference, shrinkage, variational approximation, empirical Bayes

Journal Title

The Annals of Applied Statistics

Conference Name

Journal ISSN

1932-6157
1941-7330

Volume Title

11

Publisher

Institute of Mathematical Statistics
Sponsorship
This work was supported by the Center for Medical Systems Biology (CMSB), and the European Union Grant EpiRadBio, established by the Netherlands Genomics Initiative/Netherlands Organization for Scientific Research (NGI/NWO), nr. FP7-269553.