Abstract #300422

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JSM 2002 Abstract #300422
Activity Number: 300
Type: Invited
Date/Time: Wednesday, August 14, 2002 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract - #300422
Title: Degrees of Boosting
Author(s): Andreas Buja*+
Affiliation(s): AT&T Labs - Research
Address: 180 Park Ave, Florham Park, NJ, 07932-1004,
Keywords:
Abstract:

Motivated by the Annals paper by Friedman, Hastie and Tibshirani on boosting classifiers, we investigate the role and structure of loss functions in classification problems. We show that all common classification loss functions share a consistency property that is known in subjective probability as being a "proper scoring rule." By coincidence of naming, all classifiers based on proper scoring rules permit Fisher scoring algorithms for fitting models. We give evidence that Freud and Schapire's exponential loss is a more drastic booster than logistic loss, which in turn is more drastic than squared error loss on the probability scale; and all boost more strongly than misclassification rate. For two classes, most loss functions yield quite similar results, but for more than two classes differences start to emerge.

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Revised March 2002