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Kronecker determinantal point processes

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NIPS-2016-kronecker-determinantal-point-processes-Paper.pdf

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Date Issued
December 2016
Journal
Advances in Neural Information Processing Systems
Citation
2016. "Kronecker determinantal point processes." Advances in Neural Information Processing Systems, 0.
Version
Final published version
Abstract
© 2016 NIPS Foundation - All Rights Reserved. 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(N3) 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.
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