A Mixture Copula Bayesian Network Model for Multimodal Genomic Data

Abstract

Gaussian Bayesian networks have become a widely used framework to estimate directed associations between joint Gaussian variables, where the network structure encodes decomposition of multivariate normal density into local terms. However, the resulting estimates can be inaccurate when normality assumption is moderately or severely violated, making it unsuitable to deal with recent genomic data such as the Cancer Genome Atlas data. In the present paper, we propose a mixture copula Bayesian network model which provides great flexibility in modeling non-Gaussian and multimodal data for causal inference. The parameters in mixture copula functions can be efficiently estimated by a routine Expectation-Maximization algorithm. A heuristic search algorithm based on Bayesian information criterion is developed to estimate the network structure, and prediction can be further improved by the best-scoring network out of multiple predictions from random initial values. Our method outperforms Gaussian Bayesian networks and regular copula Bayesian networks in terms of modeling flexibility and prediction accuracy, as demonstrated using a cell signaling dataset. We apply the proposed methods to the Cancer Genome Atlas data to study the genetic and epigenetic pathways that underlie serous ovarian cancer.

Constructing gene regulatory networks from microarray data using non-Gaussian pair-copula Bayesian networks

“…Nevertheless, such techniques are unable to deal with non-normality, multi-modality and heavy tailedness that are commonly seen in current massive genetic data. In fact, the resulting estimates can be inaccurate when the normality assumption is moderately or severely violated, making the techniques unsuitable for dealing with genetic data 16 . To relax this limitative constraint, one can apply copula function which is a multivariate cumulative distribution function ws-jbcb Constructing gene regulatory networks .... 3 and marginal probability distribution of each variable is uniform.…”

“…The combination of copula with graphical model constructs multivariate distribution with univariate marginals and a copula function C that links the marginals. However, the regular copula functions such as Gaussian copula may not be able to accurately depict multi-modal joint distributions in the genomic data 16 . In addition, the non-Gaussian probabilistic graphical model is subject to selection of a copula function for each local term.…”