On Surrogate Loss Functions, f-Divergences and Decentralized Detection
published: July 30, 2009, recorded: June 2009, views: 931
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In 1951, David Blackwell published a seminal paper - widely cited in economics - in which a link was established between the risk based on 0-1 loss and a class of functionals known as f-divergences. The latter functionals have since come to play an important role in several areas of signal processing and information theory, including decentralized detection. Yet their role in these fields has largely been heuristic. We show that an extension of Blackwell´s programme provides a solid foundation for the use of f-divergences in decentralized detection, as well as in more general problems of experimental design. Our extension is based on a connection between f-divergences and the class of so-called surrogate loss funcions - computationally-inspired upper bounds on 0-1 loss that have become central in the machine learning literature on classification. (Joint work with XuanLong Nguyen and Martin Wainwright.)
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