Directed Graphical Models and Causal Discovery for Zero-Inflated Data

TL;DR

This paper introduces a novel directed graphical modeling approach tailored for zero-inflated single-cell RNA sequencing data, enabling accurate inference of gene regulatory networks despite data sparsity.

Contribution

It develops a new zero-inflated model based on Hurdle distributions that can identify the exact causal graph under weak assumptions, with practical graph recovery methods.

Findings

Successfully applied to real T helper cell data

Validated identifiability through simulations

Achieved accurate graph estimation in zero-inflated context

Abstract

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.