Divergence Frontiers for Generative Models: Sample Complexity, Quantization Effects, and Frontier Integrals
This work provides quantitative tools for measuring the statistical performance of generative models, addressing a key need in machine learning evaluation.
The paper tackles the problem of evaluating deep generative models by establishing non-asymptotic bounds on the sample complexity of divergence frontiers and introducing frontier integrals as summary statistics, with results showing faster convergence rates using smoothed estimators.
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.