A direct method for estimating a causal ordering in a linear non-Gaussian acyclic model

TL;DR

This paper introduces a direct, parameter-free method for estimating causal orderings in linear non-Gaussian acyclic models, guaranteeing convergence and improving over iterative algorithms.

Contribution

It presents a novel direct estimation algorithm that reliably finds the causal ordering without iterative search or prior network knowledge.

Findings

Algorithm converges to the correct solution in a fixed number of steps.

No algorithmic parameters are required for the method.

Outperforms iterative search methods in accuracy and efficiency.

Abstract

Structural equation models and Bayesian networks have been widely used to analyze causal relations between continuous variables. In such frameworks, linear acyclic models are typically used to model the datagenerating process of variables. Recently, it was shown that use of non-Gaussianity identifies a causal ordering of variables in a linear acyclic model without using any prior knowledge on the network structure, which is not the case with conventional methods. However, existing estimation methods are based on iterative search algorithms and may not converge to a correct solution in a finite number of steps. In this paper, we propose a new direct method to estimate a causal ordering based on non-Gaussianity. In contrast to the previous methods, our algorithm requires no algorithmic parameters and is guaranteed to converge to the right solution within a small fixed number of steps if the data strictly follows the model.