Biwei Huang: Latent Hierarchical Causal Structure Discovery with Rank Constraints

Biwei Huang (UC San Diego): Latent Hierarchical Causal Structure Discovery with Rank Constraints
- Discussant: Erich Kummerfeld (University of Minnesota)- Abstract: Most causal discovery procedures assume that there are no latent confounders in the system, which is often violated in real-world problems. In this talk, 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.