Low-Rank Factorization of Determinantal Point Processes for Recommendation

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 predictive performance than prior full-rank DPP approaches, and better performance than several other competing recommendation methods in many cases. We conduct an extensive experimental evaluation using several real-world datasets in the domain of product recommendation to demonstrate the utility of our method, along with its limitations.

arXiv comment10 pages, 4 figures. Submitted to KDD 2016

References in corpus (3)

• Determinantal point processes for machine learning
• Learning Determinantal Point Processes
• Learning Mixtures of Submodular Shells with Application to Document Summarization

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• Kronecker Determinantal Point Processes
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• DPPy: Sampling DPPs with Python
• The Bayesian Low-Rank Determinantal Point Process Mixture Model