Bayesian inference for multiple Gaussian graphical models with application to metabolic association networks

TL;DR

This paper develops a Bayesian framework using multiplicative priors and SMC algorithms for joint inference of multiple Gaussian graphical models, applied to analyze metabolic networks affected by cadmium exposure.

Contribution

It introduces a novel Bayesian approach with multiplicative priors for multiple GGMs, enabling joint inference and analysis of metabolic association networks under different conditions.

Findings

Identified significant changes in metabolite interactions due to cadmium exposure.

Proposed a flexible prior model that encourages sparsity or specific degree distributions.

Developed an SMC algorithm for efficient posterior estimation of multiple GGMs.

Abstract

We investigate the effect of cadmium (a toxic environmental pollutant) on the correlation structure of a number of urinary metabolites using Gaussian graphical models (GGMs). The inferred metabolic associations can provide important information on the physiological state of a metabolic system and insights on complex metabolic relationships. Using the fitted GGMs, we construct differential networks, which highlight significant changes in metabolite interactions under different experimental conditions. The analysis of such metabolic association networks can reveal differences in the underlying biological reactions caused by cadmium exposure. We consider Bayesian inference and propose using the multiplicative (or Chung-Lu random graph) model as a prior on the graphical space. In the multiplicative model, each edge is chosen independently with probability equal to the product of the connectivities of the end nodes. This class of prior is parsimonious yet highly flexible; it can be used to encourage sparsity or graphs with a pre-specified degree distribution when such prior knowledge is available. We extend the multiplicative model to multiple GGMs linking the probability of edge inclusion through logistic regression and demonstrate how this leads to joint inference for multiple GGMs. A sequential Monte Carlo (SMC) algorithm is developed for estimating the posterior distribution of the graphs.