TopP&R: Robust Support Estimation Approach for Evaluating Fidelity and Diversity in Generative Models

We propose a robust and reliable evaluation metric for generative models called Topological Precision and Recall (TopP&R, pronounced "topper"), which systematically estimates supports by retaining only topologically and statistically significant features with a certain level of confidence. Existing metrics, such as Inception Score (IS), Frechet Inception Distance (FID), and various Precision and Recall (P&R) variants, rely heavily on support estimates derived from sample features. However, the reliability of these estimates has been overlooked, even though the quality of the evaluation hinges entirely on their accuracy. In this paper, we demonstrate that current methods not only fail to accurately assess sample quality when support estimation is unreliable, but also yield inconsistent results. In contrast, TopP&R reliably evaluates the sample quality and ensures statistical consistency in its results. Our theoretical and experimental findings reveal that TopP&R provides a robust evaluation, accurately capturing the true trend of change in samples, even in the presence of outliers and non-independent and identically distributed (Non-IID) perturbations where other methods result in inaccurate support estimations. To our knowledge, TopP&R is the first evaluation metric specifically focused on the robust estimation of supports, offering statistical consistency under noise conditions.