Convexity of Proper Composite Binary Losses

Mark Reid, Robert Williamson
Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, PMLR 9:637-644, 2010.

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 this Paper

BibTeX
@InProceedings{pmlr-v9-reid10a, 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}, pages = {637--644}, year = {2010}, editor = {Teh, Yee Whye and Titterington, Mike}, volume = {9}, series = {Proceedings of Machine Learning Research}, address = {Chia Laguna Resort, Sardinia, Italy}, month = {13--15 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v9/reid10a/reid10a.pdf}, url = {https://proceedings.mlr.press/v9/reid10a.html}, 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.} }
Endnote
%0 Conference Paper %T Convexity of Proper Composite Binary Losses %A Mark Reid %A Robert Williamson %B Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2010 %E Yee Whye Teh %E Mike Titterington %F pmlr-v9-reid10a %I PMLR %P 637--644 %U https://proceedings.mlr.press/v9/reid10a.html %V 9 %X 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.
RIS
TY - CPAPER TI - Convexity of Proper Composite Binary Losses AU - Mark Reid AU - Robert Williamson BT - Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics DA - 2010/03/31 ED - Yee Whye Teh ED - Mike Titterington ID - pmlr-v9-reid10a PB - PMLR DP - Proceedings of Machine Learning Research VL - 9 SP - 637 EP - 644 L1 - http://proceedings.mlr.press/v9/reid10a/reid10a.pdf UR - https://proceedings.mlr.press/v9/reid10a.html AB - 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. ER -
APA
Reid, M. & Williamson, R.. (2010). Convexity of Proper Composite Binary Losses. Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 9:637-644 Available from https://proceedings.mlr.press/v9/reid10a.html.

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