Causal Discovery with Latent Confounders Based on Higher-Order Cumulants

TL;DR

This paper introduces a novel method for causal discovery in the presence of latent confounders using higher-order cumulants, providing a practical algorithm with proven asymptotic correctness.

Contribution

It develops a new approach leveraging higher-order cumulants for causal discovery with latent variables, extending from single to multiple latent components.

Findings

The method accurately identifies causal structures with latent confounders.

It demonstrates asymptotic correctness in experiments.

The approach is computationally efficient compared to existing methods.

Abstract

Causal discovery with latent confounders is an important but challenging task in many scientific areas. Despite the success of some overcomplete independent component analysis (OICA) based methods in certain domains, they are computationally expensive and can easily get stuck into local optima. We notice that interestingly, by making use of higher-order cumulants, there exists a closed-form solution to OICA in specific cases, e.g., when the mixing procedure follows the One-Latent-Component structure. In light of the power of the closed-form solution to OICA corresponding to the One-Latent-Component structure, we formulate a way to estimate the mixing matrix using the higher-order cumulants, and further propose the testable One-Latent-Component condition to identify the latent variables and determine causal orders. By iteratively removing the share identified latent components, we successfully extend the results on the One-Latent-Component structure to the Multi-Latent-Component structure and finally provide a practical and asymptotically correct algorithm to learn the causal structure with latent variables. Experimental results illustrate the asymptotic correctness and effectiveness of the proposed method.