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# A Taxonomy for Inference in Causal Model Families

Oct 2021

Neurally-parameterized Structural Causal Models in the Pearlian notion tocausality, referred to as NCM, were recently introduced as a step towardsnext-generation learning systems. However, said NCM are only concerned with thelearning aspect of causal inference but totally miss out on the architectureaspect. That is, actual causal inference within NCM is intractable in that theNCM won't return an answer to a query in polynomial time. This insight followsas corollary to the more general statement on the intractability of arbitrarySCM parameterizations, which we prove in this work through classical 3-SATreduction. Since future learning algorithms will be required to deal with bothhigh dimensional data and highly complex mechanisms governing the data, weultimately believe work on tractable inference for causality to be decisive. Wealso show that not all causal'' models are created equal. More specifically,there are models capable of answering causal queries that are not SCM, which werefer to as \emph{partially causal models} (PCM). We provide a tabular taxonomyin terms of tractability properties for all of the different model families,namely correlation-based, PCM and SCM. To conclude our work, we also providesome initial ideas on how to overcome parts of the intractability of causalinference with SCM by showing an example of how parameterizing an SCM with SPNmodules can at least allow for tractable mechanisms. We hope that our impossibility result alongside the taxonomy for tractabilityin causal models can raise awareness for this novel research direction sinceachieving success with causality in real world downstream tasks will not onlydepend on learning correct models as we also require having the practicalability to gain access to model inferences.

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