We sincerely thank all the reviewers for their feedback indicating that we present an innovative work that could have a

We address the reviewer comments below. R1: More discussion about how this idea could be applied to other generative models. Belief Propagation messages, then the model would also be able to run on discrete variables. Currently, in the paper, we only show the plots for J=1 and J=2 expansion terms. Therefore, we don't see as a limitation the fact that the functional form is Given the functional form, our method has the advantage to combine it with deep learning. R2: Missing citation to related work: http://proceedings.mlr