jmlr jmlr2012 jmlr2012-26 jmlr2012-26-reference knowledge-graph by maker-knowledge-mining
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Author: Zhihua Zhang, Dehua Liu, Guang Dai, Michael I. Jordan
Abstract: Support vector machines (SVMs) naturally embody sparseness due to their use of hinge loss functions. However, SVMs can not directly estimate conditional class probabilities. In this paper we propose and study a family of coherence functions, which are convex and differentiable, as surrogates of the hinge function. The coherence function is derived by using the maximum-entropy principle and is characterized by a temperature parameter. It bridges the hinge function and the logit function in logistic regression. The limit of the coherence function at zero temperature corresponds to the hinge function, and the limit of the minimizer of its expected error is the minimizer of the expected error of the hinge loss. We refer to the use of the coherence function in large-margin classification as “C -learning,” and we present efficient coordinate descent algorithms for the training of regularized C -learning models. Keywords: large-margin classifiers, hinge functions, logistic functions, coherence functions, C learning
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