Convexity of Proper Composite Binary Losses
Abstract
A composite loss assigns a penalty to a real-valued prediction by associating the prediction with a probability via a link function then applying a class probability estimation (CPE) loss. If the risk for a composite loss is always minimised by predicting the value associated with the true class probability the composite loss is proper. We provide a novel, explicit and complete characterisation of the convexity of any proper composite loss in terms of its link and its “weight function” associated with its proper CPE loss.
Cite
Text
Reid and Williamson. "Convexity of Proper Composite Binary Losses." Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, 2010.Markdown
[Reid and Williamson. "Convexity of Proper Composite Binary Losses." Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, 2010.](https://mlanthology.org/aistats/2010/reid2010aistats-convexity/)BibTeX
@inproceedings{reid2010aistats-convexity,
title = {{Convexity of Proper Composite Binary Losses}},
author = {Reid, Mark and Williamson, Robert},
booktitle = {Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics},
year = {2010},
pages = {637-644},
volume = {9},
url = {https://mlanthology.org/aistats/2010/reid2010aistats-convexity/}
}