Convexity of proper composite binary losses

Mark D. Reid; Robert C. Williamson

Convexity of proper composite binary losses

Mark D. Reid^*, Robert C. Williamson

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	637-644
Number of pages	8
Journal	Journal of Machine Learning Research
Volume	9
Publication status	Published - 2010
Event	13th International Conference on Artificial Intelligence and Statistics, AISTATS 2010 - Sardinia, Italy Duration: 13 May 2010 → 15 May 2010

Cite this

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title = "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.",

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

year = "2010",

language = "English",

volume = "9",

pages = "637--644",

journal = "Journal of Machine Learning Research",

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publisher = "Microtome Publishing",

note = "13th International Conference on Artificial Intelligence and Statistics, AISTATS 2010 ; Conference date: 13-05-2010 Through 15-05-2010",

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T1 - Convexity of proper composite binary losses

AU - Reid, Mark D.

AU - Williamson, Robert C.

PY - 2010

Y1 - 2010

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84862287353&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:84862287353

SN - 1532-4435

VL - 9

SP - 637

EP - 644

JO - Journal of Machine Learning Research

JF - Journal of Machine Learning Research

T2 - 13th International Conference on Artificial Intelligence and Statistics, AISTATS 2010

Y2 - 13 May 2010 through 15 May 2010

ER -

Convexity of proper composite binary losses

Abstract

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