To build such useful tools for practitioners, one of the first assumption that needs to be relaxed is the causal sufficiency assumption as in a lot of real problems it is very rare to find a cause-effect problem that is not affected by hidden common confounder that can affect both variables such as age or gender.

One idea proposed in the literature is to model confounders by introducing correlation between the noise variables $N_X$ and $N_Y$ that affect $X$ and $Y$ as in or by modelling all the unobserved confounding effects by a new noise variable $N_{ XY}$ entering in the generation process of $X$ and $Y$.