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.

本文提出了一种估算过程，可以高效确定潜在变量的位置，确定它们的基数，并识别潜在的分层结构，同时考虑到多个变量之间的多条路径，使得提出的算法可以在合适的图结构限制下渐近地找到整个图的正确马尔科夫等价类。

使用排名约束的潜在分层因果结构发现