Causal Discovery on Dependent Binary Data

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 de-correlate samples of the latent utility variables, which serve as de-correlated data. Any standard causal discovery method can be applied on the de-correlated data to learn the underlying causal graph. We demonstrate that the proposed de-correlation approach significantly improves the accuracy in causal graph learning, through numerical experiments on both synthetic and real-world datasets.