LoSAM: Local Search in Additive Noise Models with Mixed Mechanisms and General Noise for Global Causal Discovery

Abstract: Inferring causal relationships from observational data is crucial when experiments are costly or infeasible. Additive noise models (ANMs) enable unique directed acyclic graph (DAG) identification, but existing sample-efficient ANM methods often rely on restrictive assumptions on the data generating process, limiting their applicability to real-world settings. We propose local search in additive noise models, LoSAM, a topological ordering method for learning a unique DAG in ANMs with mixed causal mechanisms and general noise distributions. We introduce new causal substructures and criteria for identifying roots and leaves, enabling efficient top-down learning. We prove asymptotic consistency and polynomial runtime, ensuring scalability and sample efficiency. We test LoSAM on synthetic and real-world data, demonstrating state-of-the-art performance across all mixed mechanism settings.