On divergences, surrogate loss functions, and decentralized detection

by: Xuanlong Nguyen, Martin J Wainwright, Michael I Jordan

(25 Oct 2005)

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Abstract

We develop a general correspondence between a family of loss functions that act as surrogates to 0-1 loss, and the class of Ali-Silvey or $f$-divergence functionals. This correspondence provides the basis for choosing and evaluating various surrogate losses frequently used in statistical learning (e.g., hinge loss, exponential loss, logistic loss); conversely, it provides a decision-theoretic framework for the choice of divergences in signal processing and quantization theory. We exploit this correspondence to characterize the statistical behavior of a nonparametric decentralized hypothesis testing algorithms that operate by minimizing convex surrogate loss functions. In particular, we specify the family of loss functions that are equivalent to 0-1 loss in the sense of producing the same quantization rules and discriminant functions.

@misc{citeulike:2205725, abstract = {We develop a general correspondence between a family of loss functions that act as surrogates to 0-1 loss, and the class of Ali-Silvey or \$f\$-divergence functionals. This correspondence provides the basis for choosing and evaluating various surrogate losses frequently used in statistical learning (e.g., hinge loss, exponential loss, logistic loss); conversely, it provides a decision-theoretic framework for the choice of divergences in signal processing and quantization theory. We exploit this correspondence to characterize the statistical behavior of a nonparametric decentralized hypothesis testing algorithms that operate by minimizing convex surrogate loss functions. In particular, we specify the family of loss functions that are equivalent to 0-1 loss in the sense of producing the same quantization rules and discriminant functions.}, author = {Nguyen, Xuanlong and Wainwright, Martin J. and Jordan, Michael I. }, citeulike-article-id = {2205725}, eprint = {math/0510521}, keywords = {error-estimation, loss-functions, ml-foundations}, month = {Oct}, posted-at = {2008-03-31 23:23:30}, priority = {2}, title = {On divergences, surrogate loss functions, and decentralized detection}, url = {http://arxiv.org/abs/math/0510521}, year = {2005} }

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TY - ELEC ID - citeulike:2205725 L3 - citeulike-article-id:2205725 TI - On divergences, surrogate loss functions, and decentralized detection N2 - We develop a general correspondence between a family of loss functions that act as surrogates to 0-1 loss, and the class of Ali-Silvey or $f$-divergence functionals. This correspondence provides the basis for choosing and evaluating various surrogate losses frequently used in statistical learning (e.g., hinge loss, exponential loss, logistic loss); conversely, it provides a decision-theoretic framework for the choice of divergences in signal processing and quantization theory. We exploit this correspondence to characterize the statistical behavior of a nonparametric decentralized hypothesis testing algorithms that operate by minimizing convex surrogate loss functions. In particular, we specify the family of loss functions that are equivalent to 0-1 loss in the sense of producing the same quantization rules and discriminant functions. KW - error-estimation KW - loss-functions KW - ml-foundations AU - Nguyen, Xuanlong AU - Wainwright, Martin AU - Jordan, Michael PY - 2005/Oct/25/ UR - http://arxiv.org/abs/math/0510521 ER -

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