On the Theoretical Equivalence of Several Trade-Off Curves Assessing Statistical Proximity

TL;DR

This paper unifies four different trade-off curves used to evaluate generative models, clarifying their relationships and linking them to domain adaptation bounds, thereby advancing the theoretical understanding of statistical proximity measures.

Contribution

It provides a theoretical unification of the PR, Lorenz, ROC, and Rénnyi divergence frontiers, clarifying their relationships and implications for generative model evaluation.

Findings

Unified four trade-off curves under a common framework

Established links between PR/Lorenz curves and domain adaptation bounds

Enhanced theoretical understanding of statistical proximity measures

Abstract

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 R\'enyi divergence frontiers. In addition, we discuss possible links between PR / Lorenz curves with the derivation of domain adaptation bounds.