Estimating Bayesian networks for high-dimensional data with complex mean structure and random effects

TL;DR

This paper introduces new score metrics for estimating Bayesian networks from high-dimensional data with complex mean structures and random effects, improving accuracy in biological data analysis.

Contribution

It proposes a fully Bayesian and a restricted maximum likelihood inspired score metric for Bayesian network estimation considering complex mean and variance structures.

Findings

New metrics outperform traditional methods in simulated data.

Application to grape gene expression reveals biologically meaningful relationships.

Metrics effectively account for complex mean structures in high-dimensional data.

Abstract

The estimation of Bayesian networks given high-dimensional data, in particular gene expression data, has been the focus of much recent research. Whilst there are several methods available for the estimation of such networks, these typically assume that the data consist of independent and identically distributed samples. However, it is often the case that the available data have a more complex mean structure plus additional components of variance, which must then be accounted for in the estimation of a Bayesian network. In this paper, score metrics that take account of such complexities are proposed for use in conjunction with score-based methods for the estimation of Bayesian networks. We propose firstly, a fully Bayesian score metric, and secondly, a metric inspired by the notion of restricted maximum likelihood. We demonstrate the performance of these new metrics for the estimation of Bayesian networks using simulated data with known complex mean structures. We then present the analysis of expression levels of grape berry genes adjusting for exogenous variables believed to affect the expression levels of the genes. Demonstrable biological effects can be inferred from the estimated conditional independence relationships and correlations amongst the grape-berry genes.