  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.
