Divergence Frontiers for Generative Models: Sample Complexity, Quantization Effects, and Frontier Integrals
Keywords: sample complexity, precision-recall, generative modeling, divergence frontiers
TL;DR: This paper studies the statistical behavior of the divergence frontiers and its statistical summary for evaluating generative models, where the sample complexity and the choice of quantization level are investigated.
Abstract: 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.
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