AAAI Publications, Thirty-First AAAI Conference on Artificial Intelligence

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Low-Rank Factorization of Determinantal Point Processes
Mike Gartrell, Ulrich Paquet, Noam Koenigstein

Last modified: 2017-02-13

Abstract


Determinantal point processes (DPPs) have garnered attention as an elegant probabilistic model of set diversity. They are useful for a number of subset selection tasks, including product recommendation. DPPs are parametrized by a positive semi-definite kernel matrix. In this work we present a new method for learning the DPP kernel from observed data using a low-rank factorization of this kernel. We show that this low-rank factorization enables a learning algorithm that is nearly an order of magnitude faster than previous approaches, while also providing for a method for computing product recommendation predictions that is far faster (up to 20x faster or more for large item catalogs) than previous techniques that involve a full-rank DPP kernel. Furthermore, we show that our method provides equivalent or sometimes better test log-likelihood than prior full-rank DPP approaches.

Keywords


Stochastic Processes; Determinantal Point Processes; Recommender Systems

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