Loss functions, complexities, and the Legendre transformation

Y  Kalnishkan; V  Vovk; M V  Vyugin

doi:10.1016/j.tcs.2003.11.005

Loss functions, complexities, and the Legendre transformation

Y Kalnishkan, V Vovk, M V Vyugin

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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.

Original language	English
Pages (from-to)	195-207
Number of pages	13
Journal	Theoretical Computer Science
Volume	313
Issue number	2
DOIs	https://doi.org/10.1016/j.tcs.2003.11.005
Publication status	Published - 17 Feb 2004

Keywords

on-line prediction
predictive complexity
generalized entropy
prediction with expert advice

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10.1016/j.tcs.2003.11.005

legendre.pdf
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Cite this

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