线性多树结构等式模型:结构学习和反相关关系估计 (Linear Polytree Structural Equation Models: Structural Learning and Inverse Correlation Estimation)

We are interested in the problem of learning the directed acyclic graph (DAG) when data are generated from a linear structural equation model (SEM) and the causal structure can be characterized by a polytree. Specially, under both Gaussian and sub-Gaussian models, we study the sample size conditions for the well-known Chow-Liu algorithm to exactly recover the equivalence class of the polytree, which is uniquely represented by a CPDAG. We also study the error rate for the estimation of the inverse correlation matrix under such models. Our theoretical findings are illustrated by comprehensive numerical simulations, and experiments on benchmark data also demonstrate the robustness of the method when the ground truth graphical structure can only be approximated by a polytree.

翻译：当数据来自线性结构方程模型(SEM),而因果结构可以用多树为特征时,我们有兴趣了解定向圆形图(DAG)的问题。特别是,在高山和亚高森模式下,我们研究众所周知的周柳算法的样本规模条件,以完全恢复多树的等值类别,而多树的等值以CPDAA为唯一代表。我们还研究在此类模式下估算反相关矩阵的误差率。我们的理论结论通过综合数字模拟加以说明,基准数据的实验还表明,当地面真相图形结构只能被多树所接近时,该方法是否稳健。