Learning linear acyclic causal model including Gaussian noise using ancestral relationships

TL;DR

This paper introduces a new algorithm for learning linear acyclic causal models with Gaussian noise, improving efficiency over existing methods like PC-LiNGAM by leveraging ancestral relationships.

Contribution

It presents a novel, more computationally efficient algorithm for identifying distribution-equivalence patterns in linear causal models with Gaussian disturbances.

Findings

The proposed algorithm has lower time complexity than PC-LiNGAM.

It can identify distribution-equivalence patterns even with Gaussian noise.

The method generalizes ancestral finding algorithms to Gaussian disturbances.

Abstract

This paper discusses algorithms for learning causal DAGs. The PC algorithm makes no assumptions other than the faithfulness to the causal model and can identify only up to the Markov equivalence class. LiNGAM assumes linearity and continuous non-Gaussian disturbances for the causal model, and the causal DAG defining LiNGAM is shown to be fully identifiable. The PC-LiNGAM, a hybrid of the PC algorithm and LiNGAM, can identify up to the distribution-equivalence pattern of a linear causal model, even in the presence of Gaussian disturbances. However, in the worst case, the PC-LiNGAM has factorial time complexity for the number of variables. In this paper, we propose an algorithm for learning the distribution-equivalence patterns of a linear causal model with a lower time complexity than PC-LiNGAM, using the causal ancestor finding algorithm in Maeda and Shimizu, which is generalized to account for Gaussian disturbances.