  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.
