The Annals of Applied Statistics

Joint estimation of multiple related biological networks

Chris J. Oates, Jim Korkola, Joe W. Gray, and Sach Mukherjee

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Graphical models are widely used to make inferences concerning interplay in multivariate systems. In many applications, data are collected from multiple related but nonidentical units whose underlying networks may differ but are likely to share features. Here we present a hierarchical Bayesian formulation for joint estimation of multiple networks in this nonidentically distributed setting. The approach is general: given a suitable class of graphical models, it uses an exchangeability assumption on networks to provide a corresponding joint formulation. Motivated by emerging experimental designs in molecular biology, we focus on time-course data with interventions, using dynamic Bayesian networks as the graphical models. We introduce a computationally efficient, deterministic algorithm for exact joint inference in this setting. We provide an upper bound on the gains that joint estimation offers relative to separate estimation for each network and empirical results that support and extend the theory, including an extensive simulation study and an application to proteomic data from human cancer cell lines. Finally, we describe approximations that are still more computationally efficient than the exact algorithm and that also demonstrate good empirical performance.

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Ann. Appl. Stat. Volume 8, Number 3 (2014), 1892-1919.

First available in Project Euclid: 23 October 2014

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Zentralblatt MATH identifier

Bayesian network hierarchical model belief propagation information sharing


Oates, Chris J.; Korkola, Jim; Gray, Joe W.; Mukherjee, Sach. Joint estimation of multiple related biological networks. Ann. Appl. Stat. 8 (2014), no. 3, 1892--1919. doi:10.1214/14-AOAS761.

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Supplemental materials

  • Supplementary material A: Additional results and protocols. Includes: Alternative data generating models; robustness to in-degree restriction, outliers, batch effects and nonexchangeability; ancillary information for breast cancer; inferred wild type networks for breast cancer.
  • Supplementary material B: Computational implementation. MATLAB R2014a code (serial and parallel) implementing joint network inference.