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Determinantal point processes (DPPs) have attracted significant attention inmachine learning for their ability to model subsets drawn from a large itemcollection. Recent work shows that nonsymmetric DPP (NDPP) kernels havesignificant advantages over symmetric kernels in terms of modeling power andpredictive performance. However, for an item collection of size $M$, existingNDPP learning and inference algorithms require memory quadratic in $M$ andruntime cubic (for learning) or quadratic (for inference) in $M$, making themimpractical for many typical subset selection tasks. In this work, we develop alearning algorithm with space and time requirements linear in $M$ byintroducing a new NDPP kernel decomposition. We also derive a linear-complexityNDPP maximum a posteriori (MAP) inference algorithm that applies not only toour new kernel but also to that of prior work. Through evaluation on real-worlddatasets, we show that our algorithms scale significantly better, and can matchthe predictive performance of prior work.

Scalable Learning and MAP Inference for Nonsymmetric Determinantal Point Processes