Existence and uniqueness of proper scoring rules

@article{Ovcharov2015ExistenceAU,
  title={Existence and uniqueness of proper scoring rules},
  author={Evgeni Y. Ovcharov},
  journal={Journal of Machine Learning Research},
  year={2015},
  volume={16},
  pages={2207-2230}
}
To discuss the existence and uniqueness of proper scoring rules one needs to extend the associated entropy functions as sublinear functions to the conic hull of the prediction set. In some natural function spaces, such as the Lebesgue L-spaces over R, the positive cones have empty interior. Entropy functions defined on such cones have only directional derivatives. Certain entropies may be further extended continuously to open cones in normed spaces containing signed densities. The extended… CONTINUE READING

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