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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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.
This is a Submitted version This version's date is: 17/2/2004 This item is not peer reviewed
https://repository.royalholloway.ac.uk/items/b1a6300e-7131-b85e-703a-c5750c0a0cd0/3/
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