Causal Discovery with Mixed Linear and Nonlinear Additive Noise Models: A Scalable Approach

Abstract

Estimating the structure of directed acyclic graphs (DAGs) from observational data is challenging due to the super-exponential growth of the search space with the number of nodes. Previous research primarily focuses on identifying a unique DAG under specific model constraints in linear or nonlinear scenarios. However, real-world scenarios often involve causal mechanisms with a mixture of linear and nonlinear characteristics, which has received limited attention in existing literature. Due to unidentifiability, existing algorithms relying on fully identifiable conditions may produce erroneous results. Although traditional methods like the PC algorithm can be employed to uncover such graphs, they typically yield only a Markov equivalence class. This paper introduces a novel causal discovery approach that extends beyond the Markov equivalence class, aiming to uncover as many edge directions as possible when the causal graph is not fully identifiable. Our approach exploits the second derivative of the log-likelihood in observational data, harnessing scalable machine learning approaches to approximate the score function. Overall, our approach demonstrates competitive accuracy comparable to current state-of-the-art techniques while offering a significant improvement in computational speed.