Gene regulatory network in single cells based on the Poisson log-normal model

Gene regulatory network inference is crucial for understanding the complex molecular interactions in various genetic and environmental conditions. The rapid development of single-cell RNA sequencing (scRNA-seq) technologies unprecedentedly enables gene regulatory networks inference at the single cell resolution. However, traditional graphical models for continuous data, such as Gaussian graphical models, are inappropriate for network inference of scRNA-seq's count data. Here, we model the scRNA-seq data using the multivariate Poisson log-normal (PLN) distribution and represent the precision matrix of the latent normal distribution as the regulatory network. We propose to first estimate the latent covariance matrix using a moment estimator and then estimate the precision matrix by minimizing the lasso-penalized D-trace loss function. We establish the convergence rate of the covariance matrix estimator and further establish the convergence rates and the sign consistency of the proposed PLNet estimator of the precision matrix in the high dimensional setting. The performance of PLNet is evaluated and compared with available methods using simulation and gene regulatory network analysis of scRNA-seq data.