On Classification-Calibration of Gamma-Phi Losses

Yutong Wang, Clayton Scott
Proceedings of Thirty Sixth Conference on Learning Theory, PMLR 195:4929-4951, 2023.

Abstract

Gamma-Phi losses constitute a family of multiclass classification loss functions that generalize the logistic and other common losses, and have found application in the boosting literature. We establish the first general sufficient condition for the classification-calibration (CC) of such losses. To our knowledge, this sufficient condition gives the first family of nonconvex multiclass surrogate losses for which CC has been fully justified. In addition, we show that a previously proposed sufficient condition is in fact not sufficient. This contribution highlights a technical issue that is important in the study of multiclass CC but has been neglected in priorwork.

Cite this Paper

BibTeX
@InProceedings{pmlr-v195-wang23c, title = {On Classification-Calibration of Gamma-Phi Losses}, author = {Wang, Yutong and Scott, Clayton}, booktitle = {Proceedings of Thirty Sixth Conference on Learning Theory}, pages = {4929--4951}, year = {2023}, editor = {Neu, Gergely and Rosasco, Lorenzo}, volume = {195}, series = {Proceedings of Machine Learning Research}, month = {12--15 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v195/wang23c/wang23c.pdf}, url = {https://proceedings.mlr.press/v195/wang23c.html}, abstract = {Gamma-Phi losses constitute a family of multiclass classification loss functions that generalize the logistic and other common losses, and have found application in the boosting literature. We establish the first general sufficient condition for the classification-calibration (CC) of such losses. To our knowledge, this sufficient condition gives the first family of nonconvex multiclass surrogate losses for which CC has been fully justified. In addition, we show that a previously proposed sufficient condition is in fact not sufficient. This contribution highlights a technical issue that is important in the study of multiclass CC but has been neglected in priorwork.} }
Endnote
%0 Conference Paper %T On Classification-Calibration of Gamma-Phi Losses %A Yutong Wang %A Clayton Scott %B Proceedings of Thirty Sixth Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2023 %E Gergely Neu %E Lorenzo Rosasco %F pmlr-v195-wang23c %I PMLR %P 4929--4951 %U https://proceedings.mlr.press/v195/wang23c.html %V 195 %X Gamma-Phi losses constitute a family of multiclass classification loss functions that generalize the logistic and other common losses, and have found application in the boosting literature. We establish the first general sufficient condition for the classification-calibration (CC) of such losses. To our knowledge, this sufficient condition gives the first family of nonconvex multiclass surrogate losses for which CC has been fully justified. In addition, we show that a previously proposed sufficient condition is in fact not sufficient. This contribution highlights a technical issue that is important in the study of multiclass CC but has been neglected in priorwork.
APA
Wang, Y. & Scott, C.. (2023). On Classification-Calibration of Gamma-Phi Losses. Proceedings of Thirty Sixth Conference on Learning Theory, in Proceedings of Machine Learning Research 195:4929-4951 Available from https://proceedings.mlr.press/v195/wang23c.html.

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