Causal discovery seeks to uncover the causal dependencies among variables. For this purpose, we propose an algorithm called Tensor-based Second-order Causal Discovery (TSCD). Its input is a tensor obtained from the covariance matrices of observational and interventional data. Assuming the causal dependencies follow a linear structural equation model on a directed acyclic graph (DAG), TSCD outputs the DAG and the functions on its edges, requiring only that the noise variables are uncorrelated. We also implement a version of the approach for nonlinear models. Our focus on second-order statistics (via the covariance matrices) is motivated by their statistical and computational efficiency relative to higher-order moments, their identifiability relative to first-order statistics, and that they work regardless of whether the variables are Gaussian. We show that TSCD has identifiable causal order and parameters from a number of interventions that is logarithmic in the number of variables. Experiments show that TSCD is robust to noise, competitive with existing methods, and scales to hundreds of variables.

翻译：因果发现旨在揭示变量间的因果依赖关系。为此，我们提出一种名为“基于张量的二阶因果发现”（TSCD）的算法。其输入是一个由观测数据和干预数据的协方差矩阵构成的张量。假设因果依赖关系遵循有向无环图（DAG）上的线性结构方程模型，TSCD 可输出该 DAG 及其边上的函数，仅需噪声变量互不相关。我们还针对非线性模型实现了该方法的变体。我们聚焦于二阶统计量（通过协方差矩阵）的动机在于：其一，与高阶矩相比，其在统计和计算上效率更高；其二，与一阶统计量相比，其具有可辨识性；其三，无论变量是否为高斯分布，该统计量均适用。我们证明，对于对数于变量数量的干预次数，TSCD 具有可辨识的因果顺序和参数。实验表明，TSCD 对噪声鲁棒，与现有方法相比具有竞争力，并且可扩展至数百个变量。