  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), Frechet 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.
