Vine copula graphical models in the construction of biological networks

Abstract

The copula Gaussian graphical model (CGGM) is one of the major mathematical models for high dimensional biological networks which provides a graphical representation, espe-cially, for sparse networks. Basically, this model uses a regression of the Gaussian graphical model (GGM) whose precision matrix describes the conditional dependence between the variables to estimate the coefficients of the linear regression model. The Bayesian inference for the model parameters is used to overcome the dimensional limitation of GGM under sparse networks and small sample sizes. But from the application in bench-mark data sets, it is seen that although CGGM is successful in certain systems, it may not fit well for non-normal multivariate observations. In this study, we propose the vine copulas to relax the strict normality assumption of CGGM and to describe networks from a variety of copulas alternates besides the Gaussian copula. Accordingly, we evaluate the best fitted bivariate copula distribution for every pairwise gene and compute the estimated adjacency matrix which denotes the presence of an edge between the corresponding genes. We assess the performance of our proposed approach in three network data via distinct accuracy measures by comparing the outputs with the results of the CGGM.