Network Analysis of Count Data from Mixed Populations

In applications such as gene regulatory network analysis based on single-cell RNA sequencing data, samples often come from a mixture of different populations and each population has its own unique network. Available graphical models often assume that all samples are from the same population and share the same network. One has to first cluster the samples and use available methods to infer the network for every cluster separately. However, this two-step procedure ignores uncertainty in the clustering step and thus could lead to inaccurate network estimation. Motivated by these applications, we consider the mixture Poisson log-normal model for network inference of count data from mixed populations. The latent precision matrices of the mixture model correspond to the networks of different populations and can be jointly estimated by maximizing the lasso-penalized log-likelihood. Under rather mild conditions, we show that the mixture Poisson log-normal model is identifiable and has the positive definite Fisher information matrix. Consistency of the maximum lasso-penalized log-likelihood estimator is also established. To avoid the intractable optimization of the log-likelihood, we develop an algorithm called VMPLN based on the variational inference method. Comprehensive simulation and real single-cell RNA sequencing data analyses demonstrate the superior performance of VMPLN.