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Modern RNA sequencing technologies provide gene expression measurements fromsingle cells that promise refined insights on regulatory relationships amonggenes. Directed graphical models are well-suited to explore such (cause-effect)relationships. However, statistical analyses of single cell data arecomplicated by the fact that the data often show zero-inflated expressionpatterns. To address this challenge, we propose directed graphical models thatare based on Hurdle conditional distributions parametrized in terms ofpolynomials in parent variables and their 0/1 indicators of being zero ornonzero. While directed graphs for Gaussian models are only identifiable up toan equivalence class in general, we show that, under a natural and weakassumption, the exact directed acyclic graph of our zero-inflated models can beidentified. We propose methods for graph recovery, apply our model to realsingle-cell RNA-seq data on T helper cells, and show simulated experiments thatvalidate the identifiability and graph estimation methods in practice.

Directed Graphical Models and Causal Discovery for Zero-Inflated Data