Criteria of efficiency for set-valued classification

  • Vladimir Vovk
  • Ilia Nouretdinov
  • Valentina Fedorova
  • Ivan Petej
  • Alex Gammerman
Open Access

DOI: 10.1007/s10472-017-9540-3

Cite this article as:
Vovk, V., Nouretdinov, I., Fedorova, V. et al. Ann Math Artif Intell (2017). doi:10.1007/s10472-017-9540-3


We study optimal conformity measures for various criteria of efficiency of set-valued classification in an idealised setting. This leads to an important class of criteria of efficiency that we call probabilistic and argue for; it turns out that the most standard criteria of efficiency used in literature on conformal prediction are not probabilistic unless the problem of classification is binary. We consider both unconditional and label-conditional conformal prediction.


Conformal prediction Label-conditional conformal prediction Predictive efficiency Informational efficiency 

Mathematics Subject Classification (2010)

68T05 68Q32 62G15 
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© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Computer Learning Research Centre, Department of Computer ScienceRoyal Holloway, University of LondonEghamUK
  2. 2.YandexRussia

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