We propose a robust and reliable evaluation metric for generative models by
introducing topological and statistical treatments for rigorous support
estimation. Existing metrics, such as Inception Score (IS), Fr\'echet Inception
Distance (FID), and the variants of Precision and Recall (P\&R), heavily rely
on supports that are estimated from sample features. However, the reliability
of their estimation has not been seriously discussed (and overlooked) even
though the quality of the evaluation entirely depends on it. In this paper, we
propose Topological Precision and Recall (TopP\&R, pronounced 'topper'), which
provides a systematic approach to estimating supports, retaining only
topologically and statistically important features with a certain level of
confidence. This not only makes TopP\&R strong for noisy features, but also
provides statistical consistency. Our theoretical and experimental results show
that TopP\&R is robust to outliers and non-independent and identically
distributed (Non-IID) perturbations, while accurately capturing the true trend
of change in samples. To the best of our knowledge, this is the first
evaluation metric focused on the robust estimation of the support and provides
its statistical consistency under noise.

提出了一种关于生成模型的可靠评估方法，称之为 Topological Precision and Recall（TopP&R），通过引入拓扑和统计方面的处理来进行严谨的支持估计，这不仅使得 TopP&R 更适合有噪音的特征，而且提供了统计一致性。