Gang Fang's Blog

Why is Causal Faithfulness Assumption a simplicity assumption?

My answer: because to construct a model under no such assumption, one needs to consider the observed accidental independent relationships while construction of models under the simplicity assumption doesn’t.

Critique: my answer is on the right track but it lacks details. It shows that my understanding of the assumption wasn’t deep enough. ChatGPT’s elaboration provided more insights: without the causal faithfulness assumption, a direct one-to-one mapping between observed statistical (in)dependencies and causal structure can’t be established, meaning any observed independence between variables could be due to the possibility that there is no causal path between them in the causal graph but also that there is one. In the later case, it arises due to fine-tunings (i.e., some specific parameter values cancel out the association). In a more complex case, exact cancellations among multiple variables lead to observed independencies.

Therefore, the assumption simplifies the relationship between statistical data and causal structure and hence reduces the complexity of causal models, which facilitates causal discovery where the assumption allows for more identifications of causal models without accounting for many more potential causal models involving fine-tunings and cancellations.