A majority of reviewers appreciated the novel theoretical contributions of the paper, which are mainly of a statistical/information theoretical nature. A criticism raised by one of the reviewers concerns non-convexity/hardness of the considered optimization problem. Concerning this point, the rebuttal of the authors concerning the goals of the papers, the possibility of practical heuristics, and the relation to already existing literature was found convincing, and these points should be made more explicit in the final version (as proposed by the authors)