  Determinantal point processes (DPPs) have received significant attention as
an elegant probabilistic model for discrete subset selection. Most prior work
on DPP learning focuses on maximum likelihood estimation (MLE). While efficient
and scalable, MLE approaches do not leverage any subset similarity information
and may fail to recover the true generative distribution of discrete data. In
this work, by deriving a differentiable relaxation of a DPP sampling algorithm,
we present a novel approach for learning DPPs that minimizes the Wasserstein
distance between the model and data composed of observed subsets. Through an
evaluation on a real-world dataset, we show that our Wasserstein learning
approach provides significantly improved predictive performance on a generative
task compared to DPPs trained using MLE.
