This kind of methods range from very simple class of functions with LINGAM to more complex class of functions such as PNL, with each time a trade-off between the identifiability and the generality of the proposed approach as shown in the picture.

Indeed, when the class of function is very restricted, there are fewer non identifiable cases, but the model can only successfully be used when encountering very specific observed data (such as data generated by linear mechanisms). When the class of functions becomes larger, the model becomes more general and can be used for more types of distribution, but at the cost of more non identifiable cases. In the extreme case of a completely general model without restriction on the class of mechanisms, all pairs become non identifiable.