Elastic-Net Copula Granger Causality for Inference of Biological Networks

In bioinformatics, the inference of biological networks is one of the most active research areas. It involves decoding various complex biological networks that are responsible for performing diverse functions in human body. Among these networks analysis, most of the research focus is towards understanding effective brain connectivity and gene networks in order to cure and prevent related diseases like Alzheimer and cancer respectively. However, with recent advances in data procurement technology, such as DNA microarray analysis and fMRI that can simultaneously process a large amount of data, it yields high-dimensional data sets. These high dimensional dataset analyses possess challenges for the analyst.

Traditional methods of Granger causality inference use ordinary least-squares methods for structure estimation, which confront dimensionality issues when applied to high-dimensional data. Apart from dimensionality issues, most existing methods were designed to capture only the linear inferences from time series data.

In this paper, we address the issues involved in assessing Granger causality for both linear and nonlinear high-dimensional data by proposing an elegant form of the existing LASSO-based method that we call "Elastic-Net Copula Granger causality". This method provides a more stable way to infer biological networks which has been verified using rigorous experimentation. We have compared the proposed method with the existing method and demonstrated that this new strategy outperforms the existing method on all measures: precision, false detection rate, recall, and F1 score. We have also applied both methods to real HeLa cell data and StarPlus fMRI datasets and presented a comparison of the effectiveness of both methods.