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A Scale-Free Structure Prior for Graphical Models with Applications in Functional Genomics

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  • Paul Sheridan
  • Takeshi Kamimura
  • Hidetoshi Shimodaira

Abstract

The problem of reconstructing large-scale, gene regulatory networks from gene expression data has garnered considerable attention in bioinformatics over the past decade with the graphical modeling paradigm having emerged as a popular framework for inference. Analysis in a full Bayesian setting is contingent upon the assignment of a so-called structure prior—a probability distribution on networks, encoding a priori biological knowledge either in the form of supplemental data or high-level topological features. A key topological consideration is that a wide range of cellular networks are approximately scale-free, meaning that the fraction, , of nodes in a network with degree is roughly described by a power-law with exponent between and . The standard practice, however, is to utilize a random structure prior, which favors networks with binomially distributed degree distributions. In this paper, we introduce a scale-free structure prior for graphical models based on the formula for the probability of a network under a simple scale-free network model. Unlike the random structure prior, its scale-free counterpart requires a node labeling as a parameter. In order to use this prior for large-scale network inference, we design a novel Metropolis-Hastings sampler for graphical models that includes a node labeling as a state space variable. In a simulation study, we demonstrate that the scale-free structure prior outperforms the random structure prior at recovering scale-free networks while at the same time retains the ability to recover random networks. We then estimate a gene association network from gene expression data taken from a breast cancer tumor study, showing that scale-free structure prior recovers hubs, including the previously unknown hub SLC39A6, which is a zinc transporter that has been implicated with the spread of breast cancer to the lymph nodes. Our analysis of the breast cancer expression data underscores the value of the scale-free structure prior as an instrument to aid in the identification of candidate hub genes with the potential to direct the hypotheses of molecular biologists, and thus drive future experiments.

Suggested Citation

  • Paul Sheridan & Takeshi Kamimura & Hidetoshi Shimodaira, 2010. "A Scale-Free Structure Prior for Graphical Models with Applications in Functional Genomics," PLOS ONE, Public Library of Science, vol. 5(11), pages 1-12, November.
  • Handle: RePEc:plo:pone00:0013580
    DOI: 10.1371/journal.pone.0013580
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    Cited by:

    1. Gurami Tsitsiashvili & Victor Bulgakov, 2021. "New Applied Problems in the Theory of Acyclic Digraphs," Mathematics, MDPI, vol. 10(1), pages 1-10, December.
    2. Almudevar, Anthony & LaCombe, Jason, 2012. "On the choice of prior density for the Bayesian analysis of pedigree structure," Theoretical Population Biology, Elsevier, vol. 81(2), pages 131-143.
    3. Sheridan, Paul & Yagahara, Yuichi & Shimodaira, Hidetoshi, 2012. "Measuring preferential attachment in growing networks with missing-timelines using Markov chain Monte Carlo," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 5031-5040.

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