Inferring metabolic networks using the Bayesian adaptive graphical lasso with informative priors

Abstract

Metabolic processes are essential for cellular function and survival. We are interested in inferring a metabolic network in activated microglia, a major neuroimmune cell in the brain responsible for the neuroinflammation associated with neurological diseases, based on a set of quantified metabolites. To achieve this, we apply the Bayesian adaptive graphical lasso with informative priors that incorporate known relationships between covariates. To encourage sparsity, the Bayesian graphical lasso places double exponential priors on the off-diagonal entries of the precision matrix. The Bayesian adaptive graphical lasso allows each double exponential prior to have a unique shrinkage parameter. These shrinkage parameters share a common gamma hyperprior. We extend this model to create an informative prior structure by formulating tailored hyperpriors on the shrinkage parameters. By choosing parameter values for each hyperprior that shift probability mass toward zero for nodes that are close together in a reference network, we encourage edges between covariates with known relationships. This approach can improve the reliability of network inference when the sample size is small relative to the number of parameters to be estimated. When applied to the data on activated microglia, the inferred network includes both known relationships and associations of potential interest for further investigation.

Bayesian Graphical Network Analyses Reveal Complex Biological Interactions Specific to Alzheimer's Disease

“…We used a novel Bayesian graphical network approach [34] to assess the differences between the networks, and present the identified biomarker β2M as a central network regulator. We show that by increasing the number of biomarkers in the analyses spectrum, we see stepwise increases in both the complexity of the network, and in the information provided by the interaction networks.…”

“…We then use a graphical model approach, which describes the conditional dependence relationships among random variables, in order to make inference on the protein interaction networks. Specifically we use the approach of [34] to assess the relationships between biomarkers both within and between clinical groups. This Bayesian approach is designed to simultaneously infer multiple undirected networks in situations where some networks may be unrelated, while others may have a similar structure.…”

“…This measure of similarity reflects how appropriate the assumption that the networks for any two groups have common edges is, based on the data for each group. This Bayesian approach was run using the default hyperparameter setting and posterior inference procedure as described in [34]. …”

Bayesian Inference of Multiple Gaussian Graphical Models

“…The most popular of these is the graphical lasso (Meinshausen and Bühlmann, 2006; Yuan and Lin, 2007; Friedman et al, 2008), which uses an ℓ 1 penalty on the off-diagonal entries of the precision matrix to achieve sparsity in estimation of the graph structure. Among Bayesian approaches, the Bayesian graphical lasso, proposed as the Bayesian analogue to the graphical lasso, places double exponential priors on the off-diagonal entries of the precision matrix (Wang, 2012; Peterson et al, 2013). Estimation of a sparse graph structure using the Bayesian graphical lasso is not straightforward, however, since the precision matrices sampled from the posterior distribution do not contain exact zeros.…”

Metabolomics of Neurodegenerative Diseases

“…Hence, over the years attention has shifted from lists of molecules to sets of functionally related coordinated alterations, that constitute pathways or bioprocesses, that in concert orchestrate the underlying biology at cellular or organismal level. In other words, this so-called pathwaycentric approach results in reduction of data dimensionality while preserving the interaction between the components within an experiment (Glazko & Emmert-Streib, 2009;Peterson et al, 2013). There are different approaches to define pathways using metabolomics data, some of which involve mapping metabolites to existing pathway maps and rely on enrichment methods, while others are much more sophisticated in that they explore enrichments across a larger compendia of molecular processes assembled within databases without the prerequisite for predefined pathway maps.…”