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Concentration and ROC Curves, Revisited

Author

Listed:
  • Mauro Gasparini

    (Politecnico di Torino)

  • Lidia Sacchetto

    (Politecnico di Torino)

Abstract

This work is aimed at illustrating the strict relationship between a general definition of concentration function appeared quite some time ago on this journal and a widely used measure of the diagnostic strength of a family of binary classifiers indexed by a threshold parameter, the so-called ROC curve. The ROC curve is a common work tool in Statistics, Machine Learning and Artificial Intelligence, appearing in many applications where a binary classification (diagnosis) procedure is of interest. Hence, it is worth remarking that diagnostic strength and concentration are two sides of the same coin: the higher the concentration of one probability measure with respect to another, the higher the diagnostic strength of the likelihood ratio classification rule.

Suggested Citation

  • Mauro Gasparini & Lidia Sacchetto, 2023. "Concentration and ROC Curves, Revisited," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 292-305, February.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:1:d:10.1007_s13171-021-00244-5
    DOI: 10.1007/s13171-021-00244-5
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    References listed on IDEAS

    as
    1. Edna Schechtman & Gideon Schechtman, 2019. "The relationship between Gini terminology and the ROC curve," METRON, Springer;Sapienza Università di Roma, vol. 77(3), pages 171-178, December.
    2. Mauro Gasparini & Lidia Sacchetto, 2020. "On the definition of a concentration function relevant to the ROC curve," METRON, Springer;Sapienza Università di Roma, vol. 78(3), pages 271-277, December.
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    1. Mauro Gasparini & Lidia Sacchetto, 2020. "On the definition of a concentration function relevant to the ROC curve," METRON, Springer;Sapienza Università di Roma, vol. 78(3), pages 271-277, December.

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