The Annals of Applied Statistics

Gene network reconstruction using global-local shrinkage priors

Gwenaël G. R. Leday, Mathisca C. M. de Gunst, Gino B. Kpogbezan, Aad W. van der Vaart, Wessel N. van Wieringen, and Mark A. van de Wiel

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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.

Article information

Ann. Appl. Stat., Volume 11, Number 1 (2017), 41-68.

Received: February 2016
Revised: June 2016
First available in Project Euclid: 8 April 2017

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Zentralblatt MATH identifier

Undirected gene network Bayesian inference shrinkage variational approximation empirical Bayes


Leday, Gwenaël G. R.; de Gunst, Mathisca C. M.; Kpogbezan, Gino B.; van der Vaart, Aad W.; van Wieringen, Wessel N.; van de Wiel, Mark A. Gene network reconstruction using global-local shrinkage priors. Ann. Appl. Stat. 11 (2017), no. 1, 41--68. doi:10.1214/16-AOAS990.

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Supplemental materials

  • Technical details and complementary results. We present technical and methodological details regarding the variational approximation and the different methods under comparison in Sections 3 and 4. Furthermore, complementary simulation results are provided.