Loss Functions, Complexities, and the Legendre Transformation

  • Yuri Kalnishkan
  • Michael V. Vyugin
  • Volodya Vovk
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2225)


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.


Loss Function Kolmogorov Complexity Legendre Transformation Compact Topological Space Computational Learn Theory 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Yuri Kalnishkan
    • 1
  • Michael V. Vyugin
    • 1
  • Volodya Vovk
    • 1
  1. 1.Department of Computer Science, Royal HollowayUniversity of LondonSurreyUK

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