  The spectacular success of deep generative models calls for quantitative
tools to measure their statistical performance. Divergence frontiers have
recently been proposed as an evaluation framework for generative models, due to
their ability to measure the quality-diversity trade-off inherent to deep
generative modeling. We establish non-asymptotic bounds on the sample
complexity of divergence frontiers. We also introduce frontier integrals which
provide summary statistics of divergence frontiers. We show how smoothed
estimators such as Good-Turing or Krichevsky-Trofimov can overcome the missing
mass problem and lead to faster rates of convergence. We illustrate the
theoretical results with numerical examples from natural language processing
and computer vision.
