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.

翻译：迄今为止，从观测数据中学习编码因果关系的无环有向图（DAG）在计算上仍是一个具有挑战性的问题。近期一系列研究表明，在噪声等方差假设下，以多项式时间复杂度恢复DAG是可行的。然而，这一假设排除了噪声的异方差性——异方差虽能提供更灵活的建模能力，但处理起来也更为困难。本研究针对高斯噪声下的异方差因果结构学习问题。通过利用因果机制的正态性，我们能够恢复有效的因果排序，并借助一系列条件独立性检验唯一确定因果DAG。由此产生的HOST（异方差因果结构学习）算法简洁高效，其计算复杂度随样本量和维度均呈多项式增长。此外，在涵盖受控实验与真实数据的大量实证评估中，我们提出的HOST方法在因果顺序学习与结构学习问题上均与现有最优方法不相上下。