Heteroscedastic Causal Structure Learning

TL;DR

This paper introduces HOST, a polynomial-time algorithm for learning causal DAGs from observational data with heteroscedastic Gaussian noise, expanding causal discovery capabilities beyond equal variance assumptions.

Contribution

The study presents HOST, a novel method for heteroscedastic causal structure learning that leverages Gaussian noise properties to recover causal orderings and DAGs efficiently.

Findings

HOST scales polynomially with data size and dimensions.

HOST performs competitively with state-of-the-art methods.

Extensive experiments validate HOST's effectiveness on various datasets.

Abstract

Heretofore, learning the directed acyclic graphs (DAGs) that encode the cause-effect relationships embedded in observational data is a computationally challenging problem. A recent trend of studies has shown that it is possible to recover the DAGs with polynomial time complexity under the equal variances assumption. However, this prohibits the heteroscedasticity of the noise, which allows for more flexible modeling capabilities, but at the same time is substantially more challenging to handle. In this study, we tackle the heteroscedastic causal structure learning problem under Gaussian noises. By exploiting the normality of the causal mechanisms, we can recover a valid causal ordering, which can uniquely identify the causal DAG using a series of conditional independence tests. The result is HOST (Heteroscedastic causal STructure learning), a simple yet effective causal structure learning algorithm that scales polynomially in both sample size and dimensionality. In addition, via extensive empirical evaluations on a wide range of both controlled and real datasets, we show that the proposed HOST method is competitive with state-of-the-art approaches in both the causal order learning and structure learning problems.