Bayesian differential causal directed acyclic graphs for observational zero-inflated counts with an application to two-sample single-cell data

Observational zero-inflated count data arise in a wide range of areas such as genomics. One of the common research questions is to identify causal relationships by learning the structure of a sparse directed acyclic graph (DAG). While structure learning of DAGs has been an active research area, existing methods do not adequately account for excessive zeros and therefore are not suitable for modeling zero-inflated count data. Moreover, it is often interesting to study differences in the causal networks for data collected from two experimental groups (control vs treatment). To explicitly account for zero-inflation and identify differential causal networks, we propose a novel Bayesian differential zero-inflated negative binomial DAG (DAG0) model. We prove that the causal relationships under the proposed DAG0 are fully identifiable from purely observational, cross-sectional data, using a general proof technique that is applicable beyond the proposed model. Bayesian inference based on parallel-tempered Markov chain Monte Carlo is developed to efficiently explore the multi-modal posterior landscape. We demonstrate the utility of the proposed DAG0 by comparing it with state-of-the-art alternative methods through extensive simulations. An application in a single-cell RNA-sequencing dataset generated under two experimental groups finds some interesting results that appear to be consistent with existing knowledge. A user-friendly R package that implements DAG0 is available at https://github.com/junsoukchoi/BayesDAG0.git.