Empowering differential networks using Bayesian analysis.

Jarod Smith,Mohammad Arashi,Andriëtte Bekker

doi:10.1371/journal.pone.0261193

Jarod Smith, Mohammad Arashi + Show 1 more

Open Access

https://doi.org/10.1371/journal.pone.0261193

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Abstract

Differential networks (DN) are important tools for modeling the changes in conditional dependencies between multiple samples. A Bayesian approach for estimating DNs, from the classical viewpoint, is introduced with a computationally efficient threshold selection for graphical model determination. The algorithm separately estimates the precision matrices of the DN using the Bayesian adaptive graphical lasso procedure. Synthetic experiments illustrate that the Bayesian DN performs exceptionally well in numerical accuracy and graphical structure determination in comparison to state of the art methods. The proposed method is applied to South African COVID-19 data to investigate the change in DN structure between various phases of the pandemic.

Highlights

Probabilistic networks are becoming ever-present in a multitude of scientific disciplines
The adjacency matrix associated to a graphical model G is the binary encoded p × p precision matrix where the entries of the matrix are equal to 1 if the corresponding precision matrix entry is nonzero and zero otherwise
The focus will be on the difference of two Gaussian graphical models (GGM), G1 and G2 that share the same set of nodes V

Summary

Introduction

Probabilistic networks are becoming ever-present in a multitude of scientific disciplines. If the data is assumed to be Gaussian distributed with mean μ and covariance matrix S; the precision matrix Θ ≔ {θij}, defined as the inverse of the covariance matrix Θ S−1, directly determines the conditional dependence relations and structure of the Gaussian undirected graphical model [2]. The focus will be on the difference of two Gaussian graphical models (GGM), G1 and G2 that share the same set of nodes V. The fundamental idea here is that, if two molecules interact with one another a statistical dependency between them should be observed Another application of DNs is multivariate statistical quadratic discriminant analysis [5, 6], under the Gaussian distribution assumption. As well as graphical model determination methods exist within literature. [19], propose using Kullback-Leibler divergence and cross-validation for graphical model structure estimation

Findings

Background

Discussion