TY - JOUR
T1 - Bayes-optimal scorers for bipartite ranking
AU - Menon, Aditya Krishna
AU - Williamson, Robert C.
N1 - Publisher Copyright:
© 2014 A.K. Menon & R.C. Williamson.
PY - 2014
Y1 - 2014
N2 - We address the following seemingly simple question: what is the Bayes-optimal scorer for a bipartite ranking risk? The answer to this question helps establish the consistency of the minimisation of surrogate bipartite risks, and elucidates the relationship between bipartite ranking and other established learning problems. We show that the answer is non-trivial in general, but may be easily determined for certain special cases using the theory of proper losses. Our analysis immediately establishes equivalences between several seemingly disparate risks for bipartite ranking, such as minimising a suitable class-probability estimation risk, and minimising the p-norm push risk proposed by Rudin (2009).
AB - We address the following seemingly simple question: what is the Bayes-optimal scorer for a bipartite ranking risk? The answer to this question helps establish the consistency of the minimisation of surrogate bipartite risks, and elucidates the relationship between bipartite ranking and other established learning problems. We show that the answer is non-trivial in general, but may be easily determined for certain special cases using the theory of proper losses. Our analysis immediately establishes equivalences between several seemingly disparate risks for bipartite ranking, such as minimising a suitable class-probability estimation risk, and minimising the p-norm push risk proposed by Rudin (2009).
KW - Bipartite ranking
KW - Class-probability estimation
KW - P-norm push
KW - Proper losses
UR - http://www.scopus.com/inward/record.url?scp=84939630526&partnerID=8YFLogxK
M3 - Conference article
SN - 1532-4435
VL - 35
SP - 68
EP - 106
JO - Journal of Machine Learning Research
JF - Journal of Machine Learning Research
T2 - 27th Conference on Learning Theory, COLT 2014
Y2 - 13 June 2014 through 15 June 2014
ER -