Information, Divergence and Risk for Binary Experiments
Date
2011
Authors
Reid, Mark
Williamson, Robert
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MIT Press
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 objects and in so doing identify their representation 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.
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Keywords: Classification; Divergence; Loss functions; Regret bounds; Statistical information; Machinery; Statistics Classification; Divergence; Loss functions; Regret bounds; Statistical information
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Journal of Machine Learning Research
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Journal article
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Open Access
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