NIPS Proceedingsβ

Kronecker Determinantal Point Processes

Part of: Advances in Neural Information Processing Systems 29 (NIPS 2016)

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Authors

Conference Event Type: Poster

Abstract

Determinantal Point Processes (DPPs) are probabilistic models over all subsets a ground set of N items. They have recently gained prominence in several applications that rely on diverse subsets. However, their applicability to large problems is still limited due to O(N^3) complexity of core tasks such as sampling and learning. We enable efficient sampling and learning for DPPs by introducing KronDPP, a DPP model whose kernel matrix decomposes as a tensor product of multiple smaller kernel matrices. This decomposition immediately enables fast exact sampling. But contrary to what one may expect, leveraging the Kronecker product structure for speeding up DPP learning turns out to be more difficult. We overcome this challenge, and derive batch and stochastic optimization algorithms for efficiently learning the parameters of a KronDPP.