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Latent Hierarchical Causal Structure Discovery with Rank Constraints
Biwei Huang · Charles Jia Han Low · Feng Xie · Clark Glymour · Kun Zhang

Thu Dec 01 09:00 AM -- 11:00 AM (PST) @ Hall J #730

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 may 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 and with linear causal relations.

Author Information

Biwei Huang (University of California San Diego)
Charles Jia Han Low (CMU, Carnegie Mellon University)
Feng Xie (Beijing Technology and Business University)
Clark Glymour (Carnegie Mellon University)
Kun Zhang (CMU & MBZUAI)

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