Latent Hierarchical Causal Structure Discovery with Rank Constraints
This addresses a key limitation in causal inference for real-world applications where latent confounders are common, though it is incremental as it builds on existing rank constraint methods for more complex hierarchical scenarios.
The paper tackles the problem of causal structure discovery in the presence of latent hierarchical confounders beyond tree structures, proposing an algorithm that leverages rank constraints to identify latent variables, their cardinalities, and the hierarchical graph, with asymptotic correctness under certain graph restrictions.
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.