We present a consistent and highly scalable local approach to learn the
causal structure of a linear Gaussian polytree using data from interventional
experiments with known intervention targets. Our methods first learn the
skeleton of the polytree and then orient its edges. The output is a CPDAG
representing the interventional equivalence class of the polytree of the true
underlying distribution. The skeleton and orientation recovery procedures we
use rely on second order statistics and low-dimensional marginal distributions.
We assess the performance of our methods under different scenarios in synthetic
data sets and apply our algorithm to learn a polytree in a gene expression
interventional data set. Our simulation studies demonstrate that our approach
is fast, has good accuracy in terms of structural Hamming distance, and handles
problems with thousands of nodes.

本研究介绍了一种基于干预实验数据的一致且可扩展的本地方法，用于学习线性高斯多叉树的因果结构。该方法首先学习多叉树的骨架，然后定向其边缘，输出为代表真实潜在分布的多叉树的干预等价类的 CPDAG。我们使用二阶统计和低维边缘分布来实现骨架和定向恢复过程。通过对合成数据集的不同情景进行性能评估，并将算法应用于基因表达干预数据集，我们的模拟研究表明我们的方法快速且准确度高，能处理包含数千个节点的问题。

学习带干预的线性高斯多树模型

Learning Linear Gaussian Polytree Models with Interventions

We consider the problem of learning causal directed acyclic graphs from an
observational joint distribution. One can use these graphs to predict the
outcome of interventional experiments, from which data are often not available.
We show that if the observational distribution follows a structural equation
model with an additive noise structure, the directed acyclic graph becomes
identifiable from the distribution under mild conditions. This constitutes an
interesting alternative to traditional methods that assume faithfulness and
identify only the Markov equivalence class of the graph, thus leaving some
edges undirected. We provide practical algorithms for finitely many samples,
RESIT (Regression with Subsequent Independence Test) and two methods based on
an independence score. We prove that RESIT is correct in the population setting
and provide an empirical evaluation.

研究学习因果有向无环图从观察到的联合分布，探索一种基于结构方程模型的可识别因果图的替代方法，并提供针对有限样本的实用算法和实证研究。