Eliezer_Yudkowsky comments on Fake Causality - Less Wrong
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Robin: Yes indeed. If you can find a cutset for the tree, or cluster a manageable set of variables, all is well and good. I suspect this is what happens with most real-life causal models.
But in general, finding a good non-tree method is not just NP-hard but AI-complete. It is the problem of modeling reality itself.