Composite Binary Losses

Details Composite Binary Losses Composite Binary Losses

2009-12-17

arxiv.org/abs/0912.3301v1

Statistics

Machine Learning

38 pages, 4 figures. Submitted to JMLR

Scientific paper

We study losses for binary classification and class probability estimation and extend the understanding of them from margin losses to general composite losses which are the composition of a proper loss with a link function. We characterise when margin losses can be proper composite losses, explicitly show how to determine a symmetric loss in full from half of one of its partial losses, introduce an intrinsic parametrisation of composite binary losses and give a complete characterisation of the relationship between proper losses and ``classification calibrated'' losses. We also consider the question of the ``best'' surrogate binary loss. We introduce a precise notion of ``best'' and show there exist situations where two convex surrogate losses are incommensurable. We provide a complete explicit characterisation of the convexity of composite binary losses in terms of the link function and the weight function associated with the proper loss which make up the composite loss. This characterisation suggests new ways of ``surrogate tuning''. Finally, in an appendix we present some new algorithm-independent results on the relationship between properness, convexity and robustness to misclassification noise for binary losses and show that all convex proper losses are non-robust to misclassification noise.

Affiliated with

Also associated with

No associations

Rating

Composite Binary Losses does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Composite Binary Losses, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Composite Binary Losses will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-684880