DAG-DC-ADMM: Clustering Subjects by Causal Graph Structure with High Accuracy

In complex multivariate systems, relationships among variables often vary across subjects, and ignoring this structural heterogeneity can bias analyses. To address this, researchers Honglin Du, Muxuan Liang, and Xiang Zhong propose DAG-DC-ADMM (Directed Acyclic Graph-based Dependency Clustering via Alternating Direction Method of Multipliers). The framework integrates structural equation modeling (SEM) with a smooth acyclicity constraint and a novel groupwise truncated Lasso fusion penalty (gTLP) to cluster subjects based on the similarity of their underlying causal graphs. This transforms the problem into a nonconvex optimization that simultaneously enforces sparsity, acyclicity, and structural consensus across clusters.

To solve this challenging optimization, the authors employ an adapted ADMM (Alternating Direction Method of Multipliers) tailored for difference-of-convex programs. For restricted graph structures like upper triangular adjacency matrices, the algorithm provably converges to a Karush–Kuhn–Tucker (KKT) point. Experimental evaluations demonstrate that DAG-DC-ADMM recovers cluster-specific causal structures with a high true positive rate and a low false discovery rate. This capability is crucial for discovering heterogeneous dependencies in fields like genomics, neuroscience, and finance, where subpopulation labels are often unknown or unreliable.