Simultaneous Estimation of Many Sparse Networks via Hierarchical Poisson Log-Normal Model

Single-cell RNA-sequencing (scRNA-seq) technologies have advanced our understanding of cell-type-specific gene expression networks by enabling the direct inference of conditional independence structures among genes. However, scRNA-seq data are characterized by count distributions with numerous zeros, rendering standard Gaussian-based network inference methods inadequate. To address this challenge, we propose SPLN, a hierarchical Poisson log-normal model that simultaneously estimates multiple gene networks under different conditions or across distinct samples, while leveraging shared structural information. We develop an efficient estimation procedure that combines variational expectation–maximization (EM) with the alternating direction method of multipliers (ADMM), optimized for parallel processing. Through extensive simulation studies, SPLN demonstrates superior performance over existing methods in terms of network structure recovery and parameter estimation. We illustrate its utility on two scRNA-seq datasets: one from yeast cells measured under 11 environmental conditions, and another from 13 patients with inflammatory bowel disease. In both applications, SPLN uncovers a broader range of conditional dependence networks among genes, offering deeper insights into the underlying gene expression mechanisms. Supplementary materials for this article are available online.