Divergence Frontiers for Generative Models: Sample Complexity, Quantization Level, and Frontier Integral

• URL: http://arxiv.org/abs/2106.07898v1
• Date: Tue, 15 Jun 2021 06:26:25 GMT
• Title: Divergence Frontiers for Generative Models: Sample Complexity, Quantization Level, and Frontier Integral
• Authors: Lang Liu, Krishna Pillutla, Sean Welleck, Sewoong Oh, Yejin Choi, Zaid Harchaoui
• Abstract summary: Divergence frontiers have been proposed as an evaluation framework for generative models. We establish non-asymptotic bounds on the sample complexity of the plug-in estimator of divergence frontiers. We also augment the divergence frontier framework by investigating the statistical performance of smoothed distribution estimators.
• Score: 58.434753643798224
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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. However, the statistical behavior of divergence frontiers estimated from data remains unknown to this day. In this paper, we establish non-asymptotic bounds on the sample complexity of the plug-in estimator of divergence frontiers. Along the way, we introduce a novel integral summary of divergence frontiers. We derive the corresponding non-asymptotic bounds and discuss the choice of the quantization level by balancing the two types of approximation errors arisen from its computation. We also augment the divergence frontier framework by investigating the statistical performance of smoothed distribution estimators such as the Good-Turing estimator. We illustrate the theoretical results with numerical examples from natural language processing and computer vision.

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