On Scale-Free Prior Distributions and Their Applicability in Large-Scale Network Inference with Gaussian Graphical Models

  • Paul Sheridan
  • Takeshi Kamimura
  • Hidetoshi Shimodaira
Part of the Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering book series (LNICST, volume 4)

Abstract

This paper concerns the specification, and performance, of scale-free prior distributions with a view toward large-scale network inference from small-sample data sets. We devise three scale-free priors and implement them in the framework of Gaussian graphical models. Gaussian graphical models are used in gene network inference where high-throughput data describing a large number of variables with comparatively few samples are frequently analyzed by practitioners. And, although there is a consensus that many such networks are scale-free, the modus operandi is to assign a random network prior. Simulations demonstrate that the scale-free priors outperform the random network prior at recovering scale-free trees with degree exponents near 2, such as are characteristic of many real-world systems. On the other hand, the random network prior compares favorably at recovering scale-free trees characterized by larger degree exponents.

Keywords

Bayesian inference complex networks Gaussian graphical model Markov chain Monte Carlo prior distribution scale-free “small n large p” problem small-sample inference 

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Copyright information

© ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering 2009

Authors and Affiliations

  • Paul Sheridan
    • 1
  • Takeshi Kamimura
    • 1
  • Hidetoshi Shimodaira
    • 1
  1. 1.Tokyo Institute of TechnologyMeguro-ku, TokyoJapan

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