New Math Method Finds Cause and Effect in Messy Real-World Data

A new method called MARCEDES takes on a hard problem: learning the underlying causal directed acyclic graph (DAG) structure of a structural equation model with non-Gaussian errors. Motivated by an intentionally misspecified non-Gaussian SEM with all Laplace errors, the authors introduce a mean absolute residual risk over the space of all real matrices, and show that asymptotically the risk of the true weighted causal DAG matrix is strictly smaller than that of any other matrix. To handle high-dimensional and finite-sample settings, they add row-specific sparsity penalties and a soft DAG constraint to build a continuous score function over real matrices. That turns DAG learning into an unconstrained score minimization problem solvable with gradient-based optimization, circumventing the challenges of constrained optimization. They also develop a computational algorithm to handle the non-smoothness of the score objective and to optimally tune the row-specific sparsity penalties under a generalized Bayes framework. The authors demonstrate efficiency and improved performance over existing approaches through an extensive simulation study.