Reviews: Kronecker Determinantal Point Processes

The paper can be split into three major components: i) learning algorithm, ii) sampling algorithm, iii) experiments. It represents an extension of the algorithm for learning determinantal point processes proposed in [25] and which does not assume that the DPP-kernel has the Kronecker structure. The authors overcome the issue with the additional constraint on the DPP-kernel by performing the block-coordinate ascent. In Theorem 3.2 they show that the proposed optimization method makes the objective non-decreasing (a similar result was also shown in [25] for the algorithm which does not assume the Kronecker structure of the DPP-kernel). The authors also give guidelines how to generalize the algorithm for DPP-kernels which can be represented with the Kronecker product of more than two matrices. However, for the case of more than two matrices in the Kronecker product the authors do not show the computational gains over [25] and learning without assuming the Kronecker structure (see Theorem 3.3).