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      A Simple Algorithm for Semi-supervised Learning with Improved Generalization Error Bound

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          Abstract

          In this work, we develop a simple algorithm for semi-supervised regression. The key idea is to use the top eigenfunctions of integral operator derived from both labeled and unlabeled examples as the basis functions and learn the prediction function by a simple linear regression. We show that under appropriate assumptions about the integral operator, this approach is able to achieve an improved regression error bound better than existing bounds of supervised learning. We also verify the effectiveness of the proposed algorithm by an empirical study.

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          An Explicit Description of the Reproducing Kernel Hilbert Spaces of Gaussian RBF Kernels

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            The relative value of labeled and unlabeled samples in pattern recognition with an unknown mixing parameter

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              Sparsity in multiple kernel learning

              The problem of multiple kernel learning based on penalized empirical risk minimization is discussed. The complexity penalty is determined jointly by the empirical \(L_2\) norms and the reproducing kernel Hilbert space (RKHS) norms induced by the kernels with a data-driven choice of regularization parameters. The main focus is on the case when the total number of kernels is large, but only a relatively small number of them is needed to represent the target function, so that the problem is sparse. The goal is to establish oracle inequalities for the excess risk of the resulting prediction rule showing that the method is adaptive both to the unknown design distribution and to the sparsity of the problem.
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                Author and article information

                Journal
                27 June 2012
                Article
                1206.6412
                b8dfb479-dc0b-40d3-b091-7490cfdae5f4

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Appears in Proceedings of the 29th International Conference on Machine Learning (ICML 2012)
                cs.LG stat.ML
                icml2012

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