A Bayesian Approach for Learning Gene Networks Underlying Disease Severity in COPD

Abstract

Graphs and networks provide a natural way of representing the dependency structure among variables. More and more network data are being generated from many scientific areas, including social networks, internet networks and biological networks. In biology, large-scale proteinprotein interaction and regulatory networks are now available. New statistical methods are required to effectively analyze these data and to incorporate the prior network information into analysis of the data observed on the nodes of the graphs. Besides simple summary statistics for these networks, there is a need for formal probability models on how networks are generated. Block models and models with network motifs have been developed. In biology, how to effectively incorporate the prior network information into analysis of high dimensional genomics data raises new challenges for methodological developments. There are also needs for methods that can integrate various types of data in order to infer the network structures, especially in high dimensional settings. New methods for studying how diseases spread through networks and for designing intervention strategies using the network information are also needed. A special issue of Statistics in Biosciences has been planned that will highlight statistical methods for analysis of networks and graphs and novel applications of network methods. Submissions preferably will provide methodological advances in modeling graphs and networks, in integrating network/graph information into analysis of numerical data measured on the nodes, in learning network/graph structures from various types of data.

Bayesian modeling of multiple structural connectivity networks during the progression of Alzheimer's disease

“…These methods assume that the relationships across groups are either known a priori or learned via hierarchical clustering. More flexible approaches that employ a Bayesian framework to simultaneously learn the networks for each group and the extent to which these networks are similar have been proposed in Peterson et al (2015) and Shaddox et al (2018). More specifically, Peterson et al (2015) proposed representing the inclusion of edges using latent binary indicators, and the sharing of edges across groups was encouraged via a Markov random field prior linking the indicators.…”

“…More specifically, Peterson et al (2015) proposed representing the inclusion of edges using latent binary indicators, and the sharing of edges across groups was encouraged via a Markov random field prior linking the indicators. Shaddox et al (2018) improved upon Peterson et al's (2015) study by replacing the -Wishart prior on the precision matrix within each group with a mixture prior that is more amenable to efficient sampling. However, Shaddox et al (2018) still addresses only the inclusion or exclusion of edges, without consideration of edge strength or direction.…”

“…Shaddox et al (2018) improved upon Peterson et al's (2015) study by replacing the -Wishart prior on the precision matrix within each group with a mixture prior that is more amenable to efficient sampling. However, Shaddox et al (2018) still addresses only the inclusion or exclusion of edges, without consideration of edge strength or direction.…”

“…For the analyses of this paper, we propose a Bayesian Gaussian graphical modeling approach that retains the advantages of the approaches by Peterson et al (2015) and Shaddox et al (2018) in flexibly learning cross-group similarities within a joint framework, but that accounts for the similarity of edge values across groups, rather than only the binary presence or absence of those edges. Our framework allows us to not only learn the precision matrices within each group, but also to characterize the extent of shared edge values across the groups.…”

Fast hybrid Bayesian integrative learning of multiple gene regulatory networks for type 1 diabetes

“…As an analog to regularization approaches, Bayesian approaches enhance the shared structure of multiple graphical models by employing some specific priors. For example, Peterson, Stingo and Vannucci (2015) and Shaddox et al (2016) link the estimation of graph structures via a Markov random field prior which encourages common edges. However, since this method involves repeated calculations of concentration matrices (i.e., inverse of covariance matrices), it is only applicable when the graph is not very large.…”