论文标题
潜在的分层因果结构发现具有等级约束
Latent Hierarchical Causal Structure Discovery with Rank Constraints
论文作者
论文摘要
大多数因果发现程序都假定系统中没有潜在的混杂因素，这在现实世界中经常违反。在本文中，我们考虑了因果结构识别的一个具有挑战性的方案，其中某些变量是潜在的，并且它们形成了层次图结构以生成测量变量。潜在变量的孩子可能仍然是潜在的，并且仅测量叶子节点，此外，每对变量之间可以有多个路径（即，它超出了树的结构）。我们提出了一个估计过程，该过程可以通过利用级别的缺乏限制在测得的变量上利用等级缺乏限制来有效地定位潜在变量，确定其基础性并确定潜在的层次结构。我们表明，在适当限制图形结构的情况下，提出的算法可以渐近地找到整个图形的正确Markov等效类。
Most causal discovery procedures assume that there are no latent confounders in the system, which is often violated in real-world problems. In this paper, we consider a challenging scenario for causal structure identification, where some variables are latent and they form a hierarchical graph structure to generate the measured variables; the children of latent variables may still be latent and only leaf nodes are measured, and moreover, there can be multiple paths between every pair of variables (i.e., it is beyond tree structure). We propose an estimation procedure that can efficiently locate latent variables, determine their cardinalities, and identify the latent hierarchical structure, by leveraging rank deficiency constraints over the measured variables. We show that the proposed algorithm can find the correct Markov equivalence class of the whole graph asymptotically under proper restrictions on the graph structure.
