Statistical Undecidability in Linear, Non-Gaussian Causal Models in the Presence of Latent Confounders

Gaussian, causal orientation is not identified from observational data -- even if faithfulness is satisfied (Spirtes et al., 2002). Shimizu et al. (2006) showed that acyclic, linear, non -Gaussian (LiNGAM) causal models are identified from observational data, so long as no latent confounders are present. That holds even when faithfulness fails. Genin and Mayo-Wilson (2020) refine that result: not only are causal relationships identified, but causal orientation is statistically decidable .