Multi-omics network inference with a Gaussian copula model

Inferring partial correlation networks is essential in systems biology to uncover direct interactions between biological entities. Traditional Gaussian graphical models rely on the assumption of normally distributed data; this assumption is not satisfied when dealing with multi-omics datasets comprising heterogeneous data types such as continuous and discrete variables.

We propose a novel likelihood-based approach for network inference using a Gaussian copula model with semiparametric pairwise-likelihood estimation of the latent correlation matrix. The inferred correlation structure is then inverted and regularized via the graphical lasso to recover latent partial correlations. Compared to a moment-based approach employing bridge functions, our method demonstrates significantly improved computational efficiency and estimation accuracy, particularly for discrete data with many categories and/or large values, such as count data. This result is important for biological applications, especially for the integration of RNA-seq count data. An application to a breast cancer data set from the International Cancer Genome Consortium (ICGC) successfully identified biologically relevant interactions.

The proposed approach, based on the Gaussian copula and likelihood-based estimation, provides a novel, effective and computationally efficient mathematical framework for integrative multi-omics data analysis and network inference.