Reviews: Learning Signed Determinantal Point Processes through the Principal Minor Assignment Problem

The authors' response was in many respects quite comprehensive so I am inclined to slightly revise my score. As I said, I think the results presented in the paper seem interesting and novel, however I still feel that the motivation for signed DPP's is not sufficiently studied. The example of coffee, tea and mugs is nice, but there is just not enough concrete evidence in the current discussion suggesting that the signed DPP would even do the right thing in this simple case (I'm not saying that it wouldn't, just that it was not scientifically established in any way). The authors first define the generalized DPP and then discuss the challenges that the non-symmetric DPP poses for the task of learning of a kernel matrix from i.i.d samples when using the method of moments from prior work [23]. Then, under various assumptions on the nonsymmetric kernel matrix, a learning algorithm is proposed which runs in polynomial time (the analysis follows the ideas of [23], but addresses the challenges posed by the non-symmetric nature of the kernel).