The convexity and design of composite multiclass losses

Mark D. Reid; Robert C. Williamson; Peng Sun

The convexity and design of composite multiclass losses

Mark D. Reid^*, Robert C. Williamson, Peng Sun

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Citation (Scopus)

Abstract

We consider composite loss functions for multiclass prediction comprising a proper (i.e., Fisher-consistent) loss over probability distributions and an inverse link function. We establish conditions for their (strong) convexity and explore the implications. We also show how the separation of concerns afforded by using this composite representation allows for the design of families of losses with the same Bayes risk.

Original language	English
Title of host publication	Proceedings of the 29th International Conference on Machine Learning, ICML 2012
Pages	687-694
Number of pages	8
Publication status	Published - 2012
Event	29th International Conference on Machine Learning, ICML 2012 - Edinburgh, United Kingdom Duration: 26 Jun 2012 → 1 Jul 2012

Publication series

Name	Proceedings of the 29th International Conference on Machine Learning, ICML 2012
Volume	1

Conference

Conference	29th International Conference on Machine Learning, ICML 2012
Country/Territory	United Kingdom
City	Edinburgh
Period	26/06/12 → 1/07/12

Cite this

@inproceedings{c570aecd07f848ff8ccd63deb162a1a2,

title = "The convexity and design of composite multiclass losses",

abstract = "We consider composite loss functions for multiclass prediction comprising a proper (i.e., Fisher-consistent) loss over probability distributions and an inverse link function. We establish conditions for their (strong) convexity and explore the implications. We also show how the separation of concerns afforded by using this composite representation allows for the design of families of losses with the same Bayes risk.",

author = "Reid, {Mark D.} and Williamson, {Robert C.} and Peng Sun",

year = "2012",

language = "English",

isbn = "9781450312851",

series = "Proceedings of the 29th International Conference on Machine Learning, ICML 2012",

pages = "687--694",

booktitle = "Proceedings of the 29th International Conference on Machine Learning, ICML 2012",

note = "29th International Conference on Machine Learning, ICML 2012 ; Conference date: 26-06-2012 Through 01-07-2012",

}

Reid, MD, Williamson, RC & Sun, P 2012, The convexity and design of composite multiclass losses. in Proceedings of the 29th International Conference on Machine Learning, ICML 2012. Proceedings of the 29th International Conference on Machine Learning, ICML 2012, vol. 1, pp. 687-694, 29th International Conference on Machine Learning, ICML 2012, Edinburgh, United Kingdom, 26/06/12.

The convexity and design of composite multiclass losses. / Reid, Mark D.; Williamson, Robert C.; Sun, Peng.
Proceedings of the 29th International Conference on Machine Learning, ICML 2012. 2012. p. 687-694 (Proceedings of the 29th International Conference on Machine Learning, ICML 2012; Vol. 1).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - The convexity and design of composite multiclass losses

AU - Reid, Mark D.

AU - Williamson, Robert C.

AU - Sun, Peng

PY - 2012

Y1 - 2012

N2 - We consider composite loss functions for multiclass prediction comprising a proper (i.e., Fisher-consistent) loss over probability distributions and an inverse link function. We establish conditions for their (strong) convexity and explore the implications. We also show how the separation of concerns afforded by using this composite representation allows for the design of families of losses with the same Bayes risk.

AB - We consider composite loss functions for multiclass prediction comprising a proper (i.e., Fisher-consistent) loss over probability distributions and an inverse link function. We establish conditions for their (strong) convexity and explore the implications. We also show how the separation of concerns afforded by using this composite representation allows for the design of families of losses with the same Bayes risk.

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M3 - Conference contribution

SN - 9781450312851

T3 - Proceedings of the 29th International Conference on Machine Learning, ICML 2012

SP - 687

EP - 694

BT - Proceedings of the 29th International Conference on Machine Learning, ICML 2012

T2 - 29th International Conference on Machine Learning, ICML 2012

Y2 - 26 June 2012 through 1 July 2012

ER -

The convexity and design of composite multiclass losses

Abstract

Publication series

Conference

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