Latent Hierarchical Causal Structure Discovery with Rank Constraints

About

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.

Biwei Huang, Charles Jia Han Low, Feng Xie, Clark Glymour, Kun Zhang · 2022

Related benchmarks

Task	Dataset	Result
Causal Discovery	1-Factor model	SHD1.67	25
Causal Discovery (Skeleton recovery)	1-Factor model	F1 Score93	25
Causal Discovery	Synthetic Gaussian IL2H	Causal Cluster Recovery Rate100	24
Latent Hierarchical Causal Structure Discovery	Synthetic Gaussian IL2H Structure	Metric 3 Score0.11	24
Causal Discovery	Hierarchical structure	SHD4.17	15
Causal Discovery	Synthetic Gaussian Tree	Causal Cluster Recovery Rate100	12
Latent Hierarchical Causal Structure Discovery	Synthetic Gaussian Tree Structure	Metric 30.01	12
Latent Hierarchical Causal Structure Discovery	IL2H Uniform noise	Metric 2 Score0.76	12
Latent Hierarchical Causal Structure Discovery	Tree Uniform noise	Performance Score89	12
Latent Hierarchical Causal Structure Discovery	Measurement Model Uniform noise	Discovery Score100	12