  Learning the unique directed acyclic graph corresponding to an unknown causal
model is a challenging task. Methods based on functional causal models can
identify a unique graph, but either suffer from the curse of dimensionality or
impose strong parametric assumptions. To address these challenges, we propose a
novel hybrid approach for global causal discovery in observational data that
leverages local causal substructures. We first present a topological sorting
algorithm that leverages ancestral relationships in linear structural equation
models to establish a compact top-down hierarchical ordering, encoding more
causal information than linear orderings produced by existing methods. We
demonstrate that this approach generalizes to nonlinear settings with arbitrary
noise. We then introduce a nonparametric constraint-based algorithm that prunes
spurious edges by searching for local conditioning sets, achieving greater
accuracy than current methods. We provide theoretical guarantees for
correctness and worst-case polynomial time complexities, with empirical
validation on synthetic data.
