Causal Discovery of Linear Non-Gaussian Causal Models with Unobserved Confounding
This addresses a bottleneck in causal discovery for researchers dealing with unobserved confounding, though it is incremental as it builds on prior identifiability results.
The paper tackles the problem of identifying causal effects in linear non-Gaussian models with latent confounding, where existing methods rely on overcomplete ICA and require prior knowledge of latent counts, by proposing a recursive algorithm that uses higher-order cumulants and achieves comparable performance without needing to know the number of latents in advance.
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.