Loss functions, complexities, and the Legendre transformation

Kalnishkan, Y , Vovk, V and Vyugin, M V

(2004)

Kalnishkan, Y , Vovk, V and Vyugin, M V (2004) Loss functions, complexities, and the Legendre transformation. Theoretical Computer Science, 313 (2).

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Abstract

The paper introduces a way of re-constructing a loss function from predictive complexity. We show that a loss function and expectations of the corresponding predictive complexity w.r.t. the Bernoulli distribution are related through the Legendre transformation. It is shown that if two loss functions specify the same complexity then they are equivalent in a strong sense. The expectations are also related to the so called generalised entropy.

Information about this Version

This is a Submitted version
This version's date is: 17/2/2004
This item is not peer reviewed

Link to this Version

https://repository.royalholloway.ac.uk/items/b1a6300e-7131-b85e-703a-c5750c0a0cd0/3/

Item TypeJournal Article
TitleLoss functions, complexities, and the Legendre transformation
AuthorsKalnishkan, Y
Vovk, V
Vyugin, M V
Uncontrolled Keywordson-line prediction, predictive complexity, generalized entropy, prediction with expert advice
DepartmentsFaculty of Science\Computer Science

Identifiers
doihttp://dx.doi.org/10.1016/j.tcs.2003.11.005

Deposited by Research Information System (atira) on 22-Jul-2014 in Royal Holloway Research Online.Last modified on 22-Jul-2014

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