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

TL;DR

LoSAM is a novel topological ordering method for causal discovery in additive noise models with mixed mechanisms and general noise, offering asymptotic consistency, scalability, and state-of-the-art performance.

Contribution

It introduces a new local search approach for ANMs that handles mixed mechanisms and general noise, with proven consistency and efficient top-down learning.

Findings

Achieves state-of-the-art results on synthetic data.

Demonstrates robustness across various noise and mechanism settings.

Proves asymptotic consistency and polynomial runtime.

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.