Latent Hierarchical Causal Structure Discovery with Rank Constraints

Authors

Biwei Huang, Carnegie Mellon University
Charles Low, Carnegie Mellon University
Feng Xie, Beijing Technology and Business University
Clark Glymour, Carnegie Mellon University
Kun Zhang, Carnegie Mellon University & Mohamed bin Zayed University of Artificial IntelligenceFollow

Document Type

Conference Proceeding

Publication Title

Advances in Neural Information Processing Systems

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 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.

Publication Date

12-2022

Keywords

Equivalence classes, Trees (mathematics)

Comments

IR conditions: non-described

Available at NeurIPS Proceedings site

Recommended Citation

B. Huang et al., "Latent Hierarchical Causal Structure Discovery with Rank Constraints," Advances in Neural Information Processing Systems, vol. 35, Dec 2022.