We derive here new generalization bounds, based on Rademacher Complexity theory, for model selection and error estimation of linear (kernel) classifiers, which exploit the availability of unlabeled samples. In particular, two results are obtained: the first one shows that, using the unlabeled samples, the confidence term of the conventional bound can be reduced by a factor of three; the second one shows that the unlabeled samples can be used to obtain much tighter bounds, by building localized versions of the hypothesis class containing the optimal classifier.

We derive here new generalization bounds, based on Rademacher Complexity theory, for model selection and error estimation of linear (kernel) classifiers, which exploit the availability of unlabeled samples. In particular, two results are obtained: the first one shows that, using the unlabeled samples, the confidence term of the conventional bound can be reduced by a factor of three; the second one shows that the unlabeled samples can be used to obtain much tighter bounds, by building localized versions of the hypothesis class containing the optimal classifier.

We derive here new generalization bounds, based on Rademacher Complexity theory, for model selection and error estimation of linear (kernel) classifiers, which exploit the availability of unlabeled samples. In particular, two results are obtained: the first one shows that, using the unlabeled samples, the confidence term of the conventional bound can be reduced by a factor of three; the second one shows that the unlabeled samples can be used to obtain much tighter bounds, by building localized versions of the hypothesis class containing the optimal classifier. Papers published at the Neural Information Processing Systems Conference.

Bottlenecks of binary classification from positive and unlabeled data (PU classification) are the requirements that given unlabeled patterns are drawn from the test marginal distribution, and the penalty of the false positive error is identical to the false negative error. However, such requirements are often not fulfilled in practice. In this paper, we generalize PU classification to the class prior shift and asymmetric error scenarios. Based on the analysis of the Bayes optimal classifier, we show that given a test class prior, PU classification under class prior shift is equivalent to PU classification with asymmetric error. Then, we propose two different frameworks to handle these problems, namely, a risk minimization framework and density ratio estimation framework. Finally, we demonstrate the effectiveness of the proposed frameworks and compare both frameworks through experiments using benchmark datasets.

We derive here new generalization bounds, based on Rademacher Complexity theory, for model selection and error estimation of linear (kernel) classifiers, which exploit the availability of unlabeled samples. In particular, two results are obtained: the first one shows that, using the unlabeled samples, the confidence term of the conventional bound can be reduced by a factor of three; the second one shows that the unlabeled samples can be used to obtain much tighter bounds, by building localized versions of the hypothesis class containing the optimal classifier.