Understanding how well a deep generative model captures a distribution of high-dimensional data remains an important open challenge. It is especially difficult for certain model classes, such as Generative Adversarial Networks and Diffusion Models, whose models do not admit exact likelihoods. In this work, we demonstrate that generalized empirical likelihood (GEL) methods offer a family of diagnostic tools that can identify many deficiencies of deep generative models (DGMs). We show, with appropriate specification of moment conditions, that the proposed method can identify which modes have been dropped, the degree to which DGMs are mode imbalanced, and whether DGMs sufficiently capture intra-class diversity. We show how to combine techniques from Maximum Mean Discrepancy and Generalized Empirical Likelihood to create not only distribution tests that retain per-sample interpretability, but also metrics that include label information. We find that such tests predict the degree of mode dropping and mode imbalance up to 60% better than metrics such as improved precision/recall.

翻译：理解深度生成模型如何捕捉高维数据分布仍然是一个重要的开放挑战。对于某些模型类别（如生成对抗网络和扩散模型）尤其困难，因为它们无法提供精确的似然。在本文中，我们证明广义经验似然（GEL）方法提供了一系列诊断工具，能够识别深度生成模型（DGM）的许多缺陷。我们表明，通过适当指定矩条件，所提出的方法可以识别哪些模式被丢失、DGM模式不平衡的程度，以及DGM是否充分捕捉了类内多样性。我们还展示了如何将最大均值差异和广义经验似然的技术相结合，不仅创建保留逐样本可解释性的分布测试，还生成包含标签信息的度量指标。我们发现，与改进的精确率/召回率等指标相比，此类测试对模式丢失和模式不平衡程度的预测能力提高了60%。