Causal discovery seeks to infer the underlying causal relationships among a set of variables from observational data, typically represented through a directed acyclic graph. 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. First, we propose a de-correlation-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 then extend this framework to mixed discrete and continuous data, which introduces additional modeling and computational challenges. We assume a similar latent utility model but include a thresholding mechanism to accommodate multi-level discrete data. We use a pairwise maximum likelihood approach for mixed data to estimate a covariance matrix (dependence) among units and impute the latent continuous versions of the discrete data under an EM algorithm. De-correlation and causal graph estimation is used similarly to the binary case. Simulations on both random and real graphs show our approach significantly improves causal graph recovery over standard methods on the original data. Lastly, we apply both methods to a single-cell RNA-seq (scRNA-seq) dataset to infer a gene regulatory network (GRN) in embryonic stem cells and early differentiation. We demonstrate the improvement of our de-correlated causal discovery approaches over baseline methods in terms of test data likelihood comparison. High confidence regulatory interactions predicted by our method align well with biological literature.