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Gene regulatory network inference is crucial for understanding the complexmolecular interactions in various genetic and environmental conditions. Therapid development of single-cell RNA sequencing (scRNA-seq) technologiesunprecedentedly enables gene regulatory networks inference at the single cellresolution. However, traditional graphical models for continuous data, such asGaussian graphical models, are inappropriate for network inference ofscRNA-seq's count data. Here, we model the scRNA-seq data using themultivariate Poisson log-normal (PLN) distribution and represent the precisionmatrix of the latent normal distribution as the regulatory network. We proposeto first estimate the latent covariance matrix using a moment estimator andthen estimate the precision matrix by minimizing the lasso-penalized D-traceloss function. We establish the convergence rate of the covariance matrixestimator and further establish the convergence rates and the sign consistencyof the proposed PLNet estimator of the precision matrix in the high dimensionalsetting. The performance of PLNet is evaluated and compared with availablemethods using simulation and gene regulatory network analysis of scRNA-seqdata.

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