Despite the tremendous progress in the estimation of generative models, the development of tools for diagnosing their failures and assessing their performance has advanced at a much slower pace. Recent developments have investigated metrics that quantify which parts of the true distribution are modeled well, and, on the contrary, what the model fails to capture, akin to precision and recall in information retrieval. In this paper, we present a general evaluation framework for generative models that measures the trade-off between precision and recall using Renyi divergences. Our framework provides a novel perspective on existing techniques and extends them to more general domains. As a key advantage, it allows for efficient algorithms that are directly applicable to continuous distributions directly without discretization. We further showcase the proposed techniques on a set of image synthesis models.
@cite_5: Recent advances in generative modeling have led to an increased interest in the study of statistical divergences as means of model comparison. Commonly used evaluation methods such as Frechet Inception Distance (FID) correlate well with the perceived quality of samples and they also show sensitivity to dropping modes from the target distribution. However, these metrics are unable to distinguish different failure cases since they inherently only yield one-dimensional scores. We propose a novel definition of precision and recall for distributions which disentangles the divergence into two separate dimensions. The proposed notion is intuitive, retains desirable properties, and naturally leads to an efficient algorithm that can be used to evaluate generative models. We relate this notion to total variation as well as to recent evaluation metrics such as Inception Score and FID. To demonstrate the practical utility of the proposed approach, we perform an empirical study on several variants of Generative Adversarial Networks and the Variational Autoencoder. In an extensive set of experiments, we show that the proposed metric is able to disentangle the quality of samples from the coverage of the target distribution.
The limiting case of @math We will now show that @cite_5 corresponds to the case where @math . In particular, write both @math and @math as mixtures with a shared component that should capture the space to which both assign high likelihood, and which can be used to formalize the notions of precision and recall for distributions. The union of @math and all realizable pairs @math will be denoted by @math .