a scale-free structure prior for graphical models with applications in functional genomics前无尺度结构图形化模型与应用程序的功能基因组学.pdfVIP

A Scale-Free Structure Prior for Graphical Models with Applications in Functional Genomics Paul Sheridan*, Takeshi Kamimura, Hidetoshi Shimodaira Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan 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, P(k), of nodes in a network with degree k is roughly described by a power-law P(k) !k {c with exponent c between 2 and 3. 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