A simple matrix operation called the Schur complement can extract causal structures from models that once required massive non convex optimization.
Finding cause-and-effect relationships in datasets with 1,000 variables used to be a computational nightmare. This method uses score Jacobians and algebraic operations to sort causal variables without any optimization loops. It transforms a heavy machine learning task into a straightforward linear algebra problem that runs in seconds. The speedup allows for causal discovery on scales that were previously impossible for standard hardware. Causal inference can now become a standard preprocessing step in large-scale data pipelines.
Optimization-Free Topological Sort for Causal Discovery via the Schur Complement of Score Jacobians
arXiv · 2604.25295
Continuous causal discovery typically couples representation learning with structural optimization via non-convex acyclicity penalties, which subjects solvers to local optima and restricts scalability in high-dimensional regimes. We propose a decoupled paradigm that shifts the causal discovery bottleneck from non-convex optimization to statistical score estimation. We introduce the Score-Schur Topological Sort (SSTS), an algorithm that extracts topological order directly from unconstrained gener