Our understanding is

We thank the reviewers for their insightful feedback; we address each review below. R1: "...it is known how to solve the BFE optimisation problem by double loop algorithms" "...what is meant by'they are run once..."' "...meaningless for pairwise marginals..." Agreed. We included the pairwise marginals just for completeness. "Ising model...expect that the estimation quality will degrade with the (average) interaction strength." "The experiments have in my view a preliminary character" We agree our experiments are on small datasets.