Causal Discovery on Dependent Binary Data
Alex Chen, Qing Zhou
TL;DR
This work tackles causal discovery when observations are dependent binaries, introducing a latent utility model with unit-wise dependence captured by a covariance matrix $\Sigma$. It develops a pairwise maximum likelihood covariance estimator and an EM-like latent-data recovery with decorrelation via the Cholesky factor of $\Sigma^{-1}$, enabling standard DAG learning on decorrelated surrogates $Z$. The approach yields improved structure-learning accuracy over methods assuming independence, demonstrated on synthetic data and real scRNA-seq GRN tasks. The method is practical, scalable to $p>n$, and integrates with existing causal discovery tools to uncover underlying causal graphs in dependent datasets.
Abstract
The assumption of independence between observations (units) in a dataset is prevalent across various methodologies for learning causal graphical models. However, this assumption often finds itself in conflict with real-world data, posing challenges to accurate structure learning. We propose a decorrelation-based approach for causal graph learning on dependent binary data, where the local conditional distribution is defined by a latent utility model with dependent errors across units. We develop a pairwise maximum likelihood method to estimate the covariance matrix for the dependence among the units. Then, leveraging the estimated covariance matrix, we develop an EM-like iterative algorithm to generate and decorrelate samples of the latent utility variables, which serve as decorrelated data. Any standard causal discovery method can be applied on the decorrelated data to learn the underlying causal graph. We demonstrate that the proposed decorrelation approach significantly improves the accuracy in causal graph learning, through numerical experiments on both synthetic and real-world datasets.