The theorems in this post all say something like “if the distribution (approximately) factors according to <some DAGs>, then it also (approximately) factors according to <some other DAGs>”
So one motivating research question might be phrased as “Probability distributions have an equivalence class of Bayes nets / causal diagrams which are all compatible. But what is the structure within a given equivalence class? In particular, if we have a representative Bayes net of an equivalence class, how might we algorithmically generate other Bayes nets in that equivlance class?”
So one motivating research question might be phrased as “Probability distributions have an equivalence class of Bayes nets / causal diagrams which are all compatible. But what is the structure within a given equivalence class? In particular, if we have a representative Bayes net of an equivalence class, how might we algorithmically generate other Bayes nets in that equivlance class?”