Theoretical Equivalence of Trade-Off Curves for Statistical Proximity Assessment
Rodrigue Siry, Ryan Webster, Loic Simon, Julien Rabin; 24(185):1−34, 2023.
Abstract
The development of quantitative measures to assess the proximity of two probability distributions has been accelerated by the emergence of powerful generative models. While the scalar Frechet Inception Distance remains popular, there have been efforts to compute entire curves that depict the trade-off between fidelity and variability of the first distribution in relation to the second. Several variants of such curves have been proposed independently, and although they are intuitively similar, their relationship has not been explicitly established. To provide clarity in the field of generative evaluation, this study proposes a unification of four curves: the Precision-Recall (PR) curve, the Lorenz curve, the Receiver Operating Characteristic (ROC) curve, and a special case of Rényi divergence frontiers. Furthermore, potential connections between PR/Lorenz curves and the derivation of domain adaptation bounds are discussed.
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