A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variables

TL;DR

This paper introduces a versatile causal discovery framework that effectively identifies hidden variables and their causal relationships using rank information of covariance matrices, expanding applicability to real-world scenarios.

Contribution

The paper presents a novel rank-based causal discovery method that handles causally-related hidden variables and establishes theoretical conditions for identifiability.

Findings

RLCD accurately locates hidden variables and their causal structure.

The approach correctly identifies the Markov Equivalence Class asymptotically.

Experimental results validate effectiveness on synthetic and real data.

Abstract

Most existing causal discovery methods rely on the assumption of no latent confounders, limiting their applicability in solving real-life problems. In this paper, we introduce a novel, versatile framework for causal discovery that accommodates the presence of causally-related hidden variables almost everywhere in the causal network (for instance, they can be effects of observed variables), based on rank information of covariance matrix over observed variables. We start by investigating the efficacy of rank in comparison to conditional independence and, theoretically, establish necessary and sufficient conditions for the identifiability of certain latent structural patterns. Furthermore, we develop a Rank-based Latent Causal Discovery algorithm, RLCD, that can efficiently locate hidden variables, determine their cardinalities, and discover the entire causal structure over both measured and hidden ones. We also show that, under certain graphical conditions, RLCD correctly identifies the Markov Equivalence Class of the whole latent causal graph asymptotically. Experimental results on both synthetic and real-world personality data sets demonstrate the efficacy of the proposed approach in finite-sample cases.