ML Anthology

Loss Functions, Complexities, and the Legendre Transformation

Yuri Kalnishkan, Michael V. Vyugin, Volodya Vovk
ALT 2001 pp. 181-189
doi:10.1007/3-540-45583-3_15 /alt/2001/kalnishkan2001alt-loss/

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.

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Text

Kalnishkan et al. "Loss Functions, Complexities, and the Legendre Transformation." International Conference on Algorithmic Learning Theory, 2001. doi:10.1007/3-540-45583-3_15

Markdown

[Kalnishkan et al. "Loss Functions, Complexities, and the Legendre Transformation." International Conference on Algorithmic Learning Theory, 2001.](https://mlanthology.org/alt/2001/kalnishkan2001alt-loss/) doi:10.1007/3-540-45583-3_15

BibTeX

@inproceedings{kalnishkan2001alt-loss,
  title     = {{Loss Functions, Complexities, and the Legendre Transformation}},
  author    = {Kalnishkan, Yuri and Vyugin, Michael V. and Vovk, Volodya},
  booktitle = {International Conference on Algorithmic Learning Theory},
  year      = {2001},
  pages     = {181-189},
  doi       = {10.1007/3-540-45583-3_15},
  url       = {https://mlanthology.org/alt/2001/kalnishkan2001alt-loss/}
}