On the Theoretical Equivalence of Several Trade-Off Curves Assessing Statistical Proximity
Authors: Rodrigue Siry, Ryan Webster, Loic Simon, Julien Rabin
JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | 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. Our main contribution is the theoretical unification between the involved curves, which is summarized in the diagram of Fig. 1. The three examples are obtained by adjusting the locations, widths and weights of the Gaussian mixture models. They corresponds to scenarios of idealistic modes of deviations between the two distributions P and Q, namely (a) pure mode dropping, (b) pure mode invention and (c) pure mode reweighting. |
| Researcher Affiliation | Collaboration | Rodrigue Siry EMAIL Safran Electronics and Defense Ryan Webster EMAIL Normandie Univ, UNICAEN, ENSICAEN, CNRS, GREYC, 14000 CAEN, FRANCE Loic Simon EMAIL Normandie Univ, UNICAEN, ENSICAEN, CNRS, GREYC, 14000 CAEN, FRANCE Julien Rabin EMAIL Normandie Univ, UNICAEN, ENSICAEN, CNRS, GREYC, 14000 CAEN, FRANCE |
| Pseudocode | No | The paper does not contain any explicitly labeled pseudocode or algorithm blocks. The content is focused on mathematical definitions, theorems, and proofs. |
| Open Source Code | No | The paper mentions external links in footnotes 1 and 2 (e.g., "https://thispersondoesnotexist.com" and "https://www.kaggle.com/c/deepfake-detection-challenge"), but these are not related to the authors' own code for the methodology described in this paper. There is no explicit statement or link indicating the release of the authors' source code. |
| Open Datasets | No | The paper uses "(truncated)Gaussian mixtures" to illustrate concepts, as stated: "To make our discussion more concrete, we consider an illustrative case in Fig. 2, where P and Q are two (truncated)Gaussian mixtures." These are synthetic examples rather than publicly available datasets with concrete access information. |
| Dataset Splits | No | The paper is theoretical and does not describe experiments using real-world datasets that would require specific training, validation, or test splits. |
| Hardware Specification | No | The paper is theoretical and does not describe any experimental setup or the specific hardware used for computations. |
| Software Dependencies | No | The paper is theoretical and does not mention any software dependencies or specific version numbers for implementation. |
| Experiment Setup | No | The paper is theoretical and does not describe an experimental setup with hyperparameters or system-level training settings. |