On the Theoretical Equivalence of Several Trade-Off Curves Assessing Statistical Proximity
This work clarifies the emerging picture of generative evaluation by linking independent methods, but it is incremental as it focuses on theoretical unification without introducing new techniques.
The paper tackles the problem of unifying several trade-off curves used to assess the proximity of probability distributions in generative models, showing that four curves—precision-recall, Lorenz, ROC, and Rényi divergence frontiers—are theoretically equivalent.
The recent advent of powerful generative models has triggered the renewed development of quantitative measures to assess the proximity of two probability distributions. As the scalar Frechet inception distance remains popular, several methods have explored computing entire curves, which reveal the trade-off between the fidelity and variability of the first distribution with respect to the second one. Several of such variants have been proposed independently and while intuitively similar, their relationship has not yet been made explicit. In an effort to make the emerging picture of generative evaluation more clear, we propose a unification of four curves known respectively as: the precision-recall (PR) curve, the Lorenz curve, the receiver operating characteristic (ROC) curve and a special case of Rényi divergence frontiers. In addition, we discuss possible links between PR / Lorenz curves with the derivation of domain adaptation bounds.