Heteroscedastic Causal Structure Learning
This addresses the challenge of causal structure learning with heteroscedastic noise for researchers in causal inference, though it appears incremental as it builds on prior work under equal variances.
The authors tackled the problem of learning causal directed acyclic graphs (DAGs) from observational data under heteroscedastic noise, which allows for more flexible modeling but is computationally challenging, and they developed the HOST algorithm that scales polynomially and is competitive with state-of-the-art methods in empirical evaluations.
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.