## Information, Divergence and Risk for Binary Experiments (2009)

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Venue: | JOURNAL OF MACHINE LEARNING RESEARCH |

Citations: | 17 - 6 self |

### BibTeX

@MISC{Reid09information,divergence,

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

title = {Information, Divergence and Risk for Binary Experiments},

year = {2009}

}

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### Abstract

We unify f-divergences, Bregman divergences, surrogate regret bounds, proper scoring rules, cost curves, ROC-curves and statistical information. We do this by systematically studying integral and variational representations of these various objects and in so doing identify their primitives which all are related to cost-sensitive binary classification. As well as developing relationships between generative and discriminative views of learning, the new machinery leads to tight and more general surrogate regret bounds and generalised Pinsker inequalities relating f-divergences to variational divergence. The new viewpoint also illuminates existing algorithms: it provides a new derivation of Support Vector Machines in terms of divergences and relates Maximum Mean Discrepancy to Fisher Linear Discriminants.