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

• URL: http://arxiv.org/abs/2006.11809v3
• Date: Thu, 13 Oct 2022 13:32:19 GMT
• Title: On the Theoretical Equivalence of Several Trade-Off Curves Assessing Statistical Proximity
• Authors: Rodrigue Siry and Ryan Webster and Loic Simon and Julien Rabin
• Abstract summary: 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.
• Score: 4.626261940793027
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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