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Probabilistic Outputs for Support Vector Machines and Comparisons to Regularized Likelihood Methods
 ADVANCES IN LARGE MARGIN CLASSIFIERS
, 1999
"... The output of a classifier should be a calibrated posterior probability to enable postprocessing. Standard SVMs do not provide such probabilities. One method to create probabilities is to directly train a kernel classifier with a logit link function and a regularized maximum likelihood score. Howev ..."
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Cited by 699 (0 self)
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The output of a classifier should be a calibrated posterior probability to enable postprocessing. Standard SVMs do not provide such probabilities. One method to create probabilities is to directly train a kernel classifier with a logit link function and a regularized maximum likelihood score. However, training with a maximum likelihood score will produce nonsparse kernel machines. Instead, we train an SVM, then train the parameters of an additional sigmoid function to map the SVM outputs into probabilities. This chapter compares classification error rate and likelihood scores for an SVM plus sigmoid versus a kernel method trained with a regularized likelihood error function. These methods are tested on three dataminingstyle data sets. The SVM+sigmoid yields probabilities of comparable quality to the regularized maximum likelihood kernel method, while still retaining the sparseness of the SVM.
Generalization And Regularization in Nonlinear Learning Systems
 The Handbook of Brain Theory and Neural Networks
, 1994
"... this article we will describe generalization and regularization from the point of view of multivariate function estimation in a statistical context. Multivariate function estimation is not, in principle, distinguishable from supervised machine learning. However, until fairly recently supervised mach ..."
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Cited by 10 (3 self)
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this article we will describe generalization and regularization from the point of view of multivariate function estimation in a statistical context. Multivariate function estimation is not, in principle, distinguishable from supervised machine learning. However, until fairly recently supervised machine learning and multivariate function estimation had fairly distinct groups of practitioners, and small overlap in language, literature, and in the kinds of practical problems under study. In any case, we are given a training set, consisting of pairs of input (feature) vectors and associated outputs ft(i); y i g, for n training or example subjects, i = 1; :::n. From this data, it is desired to construct a map which generalizes well, that is, given a new value of t, the map will provide a reasonable prediction for the unobserved output associated with this t.
On the Relation Between the GACV and Joachims' ... Method for Tuning Support Vector Machines, With Extensions to the NonStandard Case
, 2001
"... We rederive a form of Joachims' ## method for tuning Support Vector Machines by the same approach as was used to derive the GACV, and show how the two methods are related. We generalize the ## method to the nonstandard case of nonrepresentative training set and unequal misclassification costs an ..."
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Cited by 2 (2 self)
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We rederive a form of Joachims' ## method for tuning Support Vector Machines by the same approach as was used to derive the GACV, and show how the two methods are related. We generalize the ## method to the nonstandard case of nonrepresentative training set and unequal misclassification costs and compare the result to the GACV estimate for the standard and nonstandard cases.