Causal Discovery on Dependent Mixed Data with Applications to Gene Regulatory Network Inference

TL;DR

This paper introduces a novel de-correlation framework for causal discovery in dependent mixed data, effectively handling both continuous and discrete variables with sample dependence, and demonstrates improved accuracy in gene regulatory network inference.

Contribution

The authors develop a structural equation model with latent variables and an EM algorithm to enable causal discovery from dependent mixed data, addressing a key gap in existing methods.

Findings

Significantly improved causal graph recovery in simulations.

Enhanced gene regulatory network inference from single-cell RNA data.

High-confidence inferred edges supported by known biology.

Abstract

Causal discovery aims to infer causal relationships among variables from observational data, typically represented by a directed acyclic graph (DAG). Most existing methods assume independent and identically distributed observations, an assumption often violated in modern applications. In addition, many datasets contain a mixture of continuous and discrete variables, which further complicates causal modeling when dependence across samples is present. To address these challenges, we propose a de-correlation framework for causal discovery from dependent mixed data. Our approach formulates a structural equation model with latent variables that accommodates both continuous and discrete variables while allowing correlated Gaussian errors across units. We estimate the dependence structure among samples via a pairwise maximum likelihood estimator for the covariance matrix and develop an EM algorithm to impute latent variables underlying discrete observations. A de-correlation transformation of the recovered latent data enables the use of standard causal discovery algorithms to learn the underlying causal graph. Simulation studies demonstrate that the proposed method substantially improves causal graph recovery compared with applying standard methods directly to the original dependent data. We apply our approach to single-cell RNA sequencing data to infer gene regulatory networks governing embryonic stem cell differentiation. The inferred regulatory networks show significantly improved predictive likelihood on test data, and many high-confidence edges are supported by known regulatory interactions reported in the literature.