Neural Information Processing Systems http://nips.cc/

Symmetric determinantal point processes (DPP) are a class of probabilistic models that encode the random selection of items that have a repulsive behavior. They have attracted a lot of attention in machine learning, where returning diverse sets of items is sought for. Sampling and learning these symmetric DPP's is pretty well understood. In this work, we consider a new class of DPP's, which we call signed DPP's, where we break the symmetry and allow attractive behaviors. We set the ground for learning signed DPP's through a method of moments, by solving the so called principal assignment problem for a class of matrices $K$ that satisfy $K_{i,j}=\pm K_{j,i}$, $i\neq j$, in polynomial time.

Sampling and learning these symmetric DPP's is pretty well understood. In this work, we consider a new class of DPP's, which we call signed DPP's, where we break the symmetry and allow attractive behaviors.

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).

Symmetric determinantal point processes (DPP) are a class of probabilistic models that encode the random selection of items that have a repulsive behavior. They have attracted a lot of attention in machine learning, where returning diverse sets of items is sought for. Sampling and learning these symmetric DPP's is pretty well understood. In this work, we consider a new class of DPP's, which we call signed DPP's, where we break the symmetry and allow attractive behaviors. We set the ground for learning signed DPP's through a method of moments, by solving the so called principal assignment problem for a class of matrices $K$ that satisfy $K_{i,j} \pm K_{j,i}$, $i eq j$, in polynomial time.

Symmetric determinantal point processes (DPP) are a class of probabilistic models that encode the random selection of items that have a repulsive behavior. They have attracted a lot of attention in machine learning, where returning diverse sets of items is sought for. Sampling and learning these symmetric DPP's is pretty well understood. In this work, we consider a new class of DPP's, which we call signed DPP's, where we break the symmetry and allow attractive behaviors. We set the ground for learning signed DPP's through a method of moments, by solving the so called principal assignment problem for a class of matrices $K$ that satisfy $K_{i,j}=\pm K_{j,i}$, $i\neq j$, in polynomial time.

Symmetric determinantal point processes (DPP) are a class of probabilistic models that encode the random selection of items that have a repulsive behavior. They have attracted a lot of attention in machine learning, where returning diverse sets of items is sought for. Sampling and learning these symmetric DPP's is pretty well understood. In this work, we consider a new class of DPP's, which we call signed DPP's, where we break the symmetry and allow attractive behaviors. We set the ground for learning signed DPP's through a method of moments, by solving the so called principal assignment problem for a class of matrices $K$ that satisfy $K_{i,j}=\pm K_{j,i}$, $i\neq j$, in polynomial time.