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# Convex risk minimization and conditional probability estimation

## Author(s): Telgarsky, M; Dudík, M; Schapire, Robert

To refer to this page use: http://arks.princeton.edu/ark:/88435/pr1524v
 Abstract: © 2015 M. Telgarsky, M. Dudík & R. Schapire. This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general enough to include cases in which no minimum exists, as occurs typically, for instance, with standard boosting algorithms. Concretely, we first show that any sequence of predictors minimizing convex risk over the source distribution will converge to this unique model when the class of predictors is linear (but potentially of infinite dimension). Secondly, we show the same result holds for empirical risk minimization whenever this class of predictors is finite dimensional, where the essential technical contribution is a norm-free generalization bound. Publication Date: 1-Jan-2015 Citation: Telgarsky, M, Dudík, M, Schapire, R. (2015). Convex risk minimization and conditional probability estimation. Journal of Machine Learning Research, 40 (2015 ISSN: 1532-4435 EISSN: 1533-7928 Type of Material: Conference Article Journal/Proceeding Title: Journal of Machine Learning Research Version: Final published version. This is an open access article.

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