The paper introduces a method for directly estimating the difference between two functional undirected graphical models, instead of doing it naively, and then combining them, the proposed method is novel, non-trivial, and leads to robust inferences. The authors provide extensive simulations to corroborate with their findings. Further, I like that even though some of the tools are well-studied and basic (e.g., fPCA), the authors generalized some key components in non-trivial fashion to make the whole thing to work. Having said that, and not taking any points from the technical contributions of the paper, I would be curious to see whether these new results would translate to the directed case, which is more related to causal inference. In particular, there’s a growing literature on the problem of ‘transportability” (e.g., [Bareinboim and Pearl, Proc. of Nat. Acad., of Sci, 2016]), which defines and builds exactly on a combined representation that overlaps two causal diagrams, which was called selection diagram. I wonder if the insights of this paper could be applied to learn this type of representation.