发表机构
The University of Melbourne（墨尔本大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种迭代识别终端节点并重构观测变量有向无环图的算法，通过稀疏加低秩分解精度矩阵处理潜在混杂变量，并给出样本复杂度保证，实验验证了理论结果。
AI 中文摘要
因果发现旨在从观测数据中恢复因果关系。在各个领域中，探索变量之间的因果关系仍然是一个重要课题，但由于潜在混杂变量的存在，这一任务变得具有挑战性。忽略这些混杂变量可能导致虚假关联和错误的边方向。在本文中，我们研究了含潜在混杂变量的线性结构方程模型。我们提出了一种算法，该算法迭代地识别终端（观测）节点并重构观测变量的有向无环图。为此，我们将观测变量的精度矩阵恢复为稀疏加低秩矩阵：稀疏矩阵捕捉观测变量之间的条件依赖性，而低秩矩阵捕捉少数潜在混杂变量的综合影响。我们证明，对于$p$个观测变量、$r$个潜在混杂变量和$s$条边，当$n \ngeqsim \nmax\{s\nlog p,\n r p\}$个样本时，我们的过程能够正确识别观测变量之间的有向因果关系。实验结果验证了我们的理论贡献。
英文摘要
Causal discovery aims to recover causal relationships from observed data. In various fields, exploring causal relationships among variables remains an important topic, but this task becomes challenging due to the existence of latent confounders. Ignoring such confounders can lead to false associations and incorrect edge directions. In this paper, we study the linear structural equation model with latent confounders. We propose an algorithm that iteratively identifies terminal (observed) nodes and reconstructs the directed acyclic graph of the observed variables. To do this, we recover the precision matrix of the observed variables as a sparse plus low-rank matrix: a sparse matrix captures the conditional dependencies among observed variables, while a low-rank matrix captures the combined influence of a few latent confounders. We establish that for $p$ observed variables, $r$ latent confounders and $s$ edges, our procedure correctly identifies the directed causal relationship among observed variables, for $n \gtrsim \max\{s\log p,\ r p\}$ samples. Experimental results validate our theoretical contributions.
