Causal Discovery of Linear Non-Gaussian Causal Models with Unobserved Confounding

TL;DR

This paper introduces a recursive algorithm for causal discovery in linear non-Gaussian models with latent confounding, overcoming limitations of ICA-based methods by not requiring prior knowledge of the number of latent variables.

Contribution

The proposed method avoids overcomplete ICA and can identify causal effects without knowing the number of latent confounders beforehand.

Findings

Achieves comparable performance to ICA-based methods

Does not require prior knowledge of latent variable count

Proven asymptotic correctness under mild assumptions

Abstract

We consider linear non-Gaussian structural equation models that involve latent confounding. In this setting, the causal structure is identifiable, but, in general, it is not possible to identify the specific causal effects. Instead, a finite number of different causal effects result in the same observational distribution. Most existing algorithms for identifying these causal effects use overcomplete independent component analysis (ICA), which often suffers from convergence to local optima. Furthermore, the number of latent variables must be known a priori. To address these issues, we propose an algorithm that operates recursively rather than using overcomplete ICA. The algorithm first infers a source, estimates the effect of the source and its latent parents on their descendants, and then eliminates their influence from the data. For both source identification and effect size estimation, we use rank conditions on matrices formed from higher-order cumulants. We prove asymptotic correctness under the mild assumption that locally, the number of latent variables never exceeds the number of observed variables. Simulation studies demonstrate that our method achieves comparable performance to overcomplete ICA even though it does not know the number of latents in advance.