# Directed Graphical Models and Causal Discovery for Zero-Inflated Data

arXiv: https://arxiv.org/abs/2004.04150 · HTML: https://mlsanity.com/paper/2004.04150/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2020.

## Built on by (most cited first, 6 of 6)

- [Recursive Causal Discovery](https://mlsanity.com/paper/2403.09300/) (2024)
- [Gene Regulatory Network Inference in the Presence of Dropouts: a Causal View](https://mlsanity.com/paper/2403.15500/) (2024)
- [Sequentially learning the topological ordering of causal directed acyclic graphs with likelihood ratio scores](https://mlsanity.com/paper/2202.01748/) (2022)
- [Learning Directed Acyclic Graphs from Partial Orderings](https://mlsanity.com/paper/2403.16031/) (2024)
- [Zero Inflation as a Missing Data Problem: a Proxy-based Approach](https://mlsanity.com/paper/2406.00549/) (2024)
- [DAG Learning from Zero-Inflated Count Data Using Continuous Optimization](https://mlsanity.com/paper/2512.16233/) (2025)

## Abstract (arXiv)

Modern RNA sequencing technologies provide gene expression measurements from single cells that promise refined insights on regulatory relationships among genes. Directed graphical models are well-suited to explore such (cause-effect) relationships. However, statistical analyses of single cell data are complicated by the fact that the data often show zero-inflated expression patterns. To address this challenge, we propose directed graphical models that are based on Hurdle conditional distributions parametrized in terms of polynomials in parent variables and their 0/1 indicators of being zero or nonzero. While directed graphs for Gaussian models are only identifiable up to an equivalence class in general, we show that, under a natural and weak assumption, the exact directed acyclic graph of our zero-inflated models can be identified. We propose methods for graph recovery, apply our model to real single-cell RNA-seq data on T helper cells, and show simulated experiments that validate the identifiability and graph estimation methods in practice.