A Characterization of Scoring Rules for Linear Properties
Abstract
We consider the design of proper scoring rules, equivalently proper losses, when the goal is to elicit some function, known as a property, of the underlying distribution. We provide a full characterization of the class of proper scoring rules when the property is linear as a function of the input distribution. A key conclusion is that any such scoring rule can be written in the form of a Bregman divergence for some convex function. We also apply our results to the design of prediction market mechanisms, showing a strong equivalence between scoring rules for linear properties and automated prediction market makers.
Cite
Text
Abernethy and Frongillo. "A Characterization of Scoring Rules for Linear Properties." Proceedings of the 25th Annual Conference on Learning Theory, 2012.Markdown
[Abernethy and Frongillo. "A Characterization of Scoring Rules for Linear Properties." Proceedings of the 25th Annual Conference on Learning Theory, 2012.](https://mlanthology.org/colt/2012/abernethy2012colt-characterization/)BibTeX
@inproceedings{abernethy2012colt-characterization,
title = {{A Characterization of Scoring Rules for Linear Properties}},
author = {Abernethy, Jacob D. and Frongillo, Rafael M.},
booktitle = {Proceedings of the 25th Annual Conference on Learning Theory},
year = {2012},
pages = {27.1-27.13},
volume = {23},
url = {https://mlanthology.org/colt/2012/abernethy2012colt-characterization/}
}